research-blogging

Single Photons Are Still Photons: "Wave-particle dualism and complementarity unraveled by a different mode"

drorzel — Mon, 04 Jun 2012 09:58:51 +0000

Single Photons Are Still Photons: "Wave-particle dualism and complementarity unraveled by a different mode"

In which we do a little ResearchBlogging, taking a look at a slightly confusing paper putting a new twist on the double-slit experiment.

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I'm off to California this afternoon, spending the rest of the week at DAMOP in Pasadena (not presenting this year, just hanging out to see the coolest new stuff in Atomic, Molecular, and Optical Physics). I don't want to leave the blog with just a cute-kid video for the whole week, though, so here's some had-core physics: a new paper in the Proceedings of the National Academy of Sciences (freely available online), looking at a new sort of double-slit experiment.

I decided to write about this, because I thought the Ars Technica write-up was a little muddled, and figured I could do better. That turns out to be hard to do, though, because the paper itself is a little muddled. I'm still not entirely sure I understand their explanation of what's going on, but I'll give it a go.

OK, so, what's this about? What do they mean "unraveled by a different mode?" Sadly, that's a title pun, and not a terribly good one. What they've done is set up a double-slit experiment that differes from past experiments in that the laser they use for it operates in a different mode than a "normal" laser.

Different mode? So, what, it works using sound waves? Gamma rays? N-Rays? "Mode" is a term of art, here, referring to the spatial profile of the laser. An "ordinary" laser produces a single round spot with a smooth profile, but that's only one possible way to run the laser, called a "TEM₀₀ mode" for reasons that don't really concern us. What they did here is to modify a laser to run in a "TEM₀₁" mode, which has a two-lobed intensity pattern like two littel dots right next to each other. They then sent this laser into a double-slit apparatus, like so:

Thanks to this laser, they were able to both determine which slit the light went through, and also see wave-like behavior on the far side, namely an interference pattern.

Wait, I thought that was impossible? Right, in the traditional double-slit, you would say that once you know that a photon passed through a particular slit, which is a particle-like behavior, you destroy any possibility of an interference pattern showing wave-like behavior. That's the "complementarity" of the title-- wave and particle descriptions are supposed to be complementary and thus mutually exclusive.

So, like, they've blown that apart completely, then? Well, not really. "Complementarity" is kind of a slippery thing. Historically, it's tended to mean whatever Niels Bohr needed it to mean in order to explain a given experiment. Since his death, its meaning hasn't gotten a whole lot clearer. What this paper really does is to point out some of that ambiguity.

What does that even mean? Let's talk about what they did, first, OK?

Sure, if it makes you happy Thank you.

What they did is to take a TEM₀₁ laser and send it into a special crystal that produces an entangled pair of photons. The distribution of these entangled photons mirrors the pump beam, so what they get out also looks kind of like a TEM₀₁ beam, with two lobes, only there are two photons in different places occupying this distribution.

So, one's in the top lobe and the other's in the bottom? No,each has its own two-lobed distribution. One photon is in either the top lobe or the bottom lobe here, the other is in either the top lobe or the bottom lobe over there. The neat trick, though, is that because the two are entangled, if the photon here is in the top lobe, the photon there will also be in the top lobe.

From Fig. 3

And this is how they know which slit the photon went through? Exactly. They use a small optical fiber to collect only the top or bottom lobe of one photon from the pair, and send the other one onto the double-slit, aligned so that the top lobe hits the top slit only, and the bottom lobe hits the bottom slit only. If they put a similar detector behind the slits, they can confirm that when they look for a photon arriving behind the slits at the same time that one hits the top/bottom detector, they only see photons in the appropriate slit, as seen in the figure at right. In this case, they're looking in the "near field," which means that the fibers to detect the photons are right behind the slit, too close to see an interference pattern.

So, how does this not destroy the interference? Well, it does while they're doing this measurement. Having used this measurement to show that the top/bottom correlation works, though, they move the detector behind the slits into the "far field," which means more or less what you expect-- far enough back to see an interference pattern. When they do that, and look at photons where they know which slit the light went through, they see an interference pattern.

And how does that make any sense at all? That's the muddled part. The interference pattern that they see has to do with the mode structure of the laser-- that is, the fact that it has the two lobes. I think that what's going on here is that due to the funny mode, the photon that goes through one of the two slits still has two components to it-- it's in a superposition of two different states corresponding to slightly different directions of travel (loosely speaking). Because of that, you can still get interference, between the two different states within the state of the single photon.

And this proves... what, exactly Well, I think you could explain it as showing that photons are still photons, even when you know which slit the photon went through. The which-slit information doesn't magically make them into classical particles forever-- they still have wave nature, due to the TEM₀₁ structure, and that wave nature is what gives you the interference.

There's got to be a "but" here, though. Yeah, which is that I'm not entirely sure I've got their explanation right. I think I understand it, but there are still some weird parts, chiefly the fact that the interference pattern they see seems to require there to be two slits. If it were purely a mode thing, I would expect to see the interference even with one of the slits blocked, but the images they show in Fig. 5 show clear interference in the two-slit case, but not the one-slit case. Which I don't understand.

They even have a puzzling statement along the same lines, writing:

This analysis shows that the interference fringes in Fig. 4 are a consequence of the TEM01 mode. Therefore, one might wonder if the mechanical double-slit is even necessary, especially because the one of the two slits is matched to the separation of the two intensity maxima of the mode. Moreover, our theoretical analysis does not contain the slits and we still obtain the fringes. Therefore, interference may be observable even without the double-slit but a substantial loss in contrast may occur.

This seems to suggest that they don't really understand it, either. But then I don't understand why they would publish it. And there's another section talking about correlations between atoms in the crystal that produces the entangled photons that I don't understand at all.

So, like I said, kind of muddled. I think it's a cute and clever demonstration experiment, but I'm still a little hazy on what it is that they've demonstrated.

So, like you said, muddled. Exactly. But kind of cool all the same. And, who knows, maybe some more expert reader will come along and leave a comment clearing things up. Or maybe they'll turn out to be presenting at DAMOP, and I can clear this up there...

Menzel, R., Puhlmann, D., Heuer, A., & Schleich, W. (2012). Wave-particle dualism and complementarity unraveled by a different mode Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1201271109

drorzel Mon, 06/04/2012 - 05:58

Tags

Experiment

Lasers

Optics

Physics

The main thing I have learnt about this so far is that PNAS will publish papers about quantum physics. That thought never occurred to me before.

Every now and then, something turns up there. It's not something I think to check regularly, but I've seen a few quantum papers show up via news sites reporting on them (as happened here...).

(Hmm, my earlier comments seems to have gotten eaten. That's what I get from trying to post from a tablet, I guess.)

I have to read the paper, but there are a couple of questions that occur to me.

First, what's the photon rate? Slow enough that they're able to detect individual photon coincidences with the detector in the near field. Is it slow enough that we can be confident that only one photon is going through at a time, or is it plausible that the photons are interfering with each other?

Second, is it possible that the entanglement gets broken before (insofar as you can use terms like "before" when talking about these sorts of quantum experiments) the photon goes through the double slits? That is, the photon that doesn't go through the slits *will* be detected as being in one or the other lobe no matter what. So, somewhere, its wavefunction collapses. For there to be anything surprising here, the two have to remain entangled so that both wavefunctions collapse together. Otherwise, if the entanglement is broken, each photon does what it does. The slit photon's wave function doesn't collapse until it hits th detection screen, and includes amplituedes from both paths, while the non-slit photon collapses when it's detected. Unless we can already be very sure that that they have to have remained entangled, it would take a Bell's-inequality-like statistical test of some sort to really show that they did in fact remain entangled, and that anything surprising is going on here.

Photons are not entangled nor interfere. Modes can do both. Photons are excitations of modes

In my unqualified opinion, what this shows is the act of measuring it self does not necessarily have to collapse the wave state. There are people out there who have been saying, "The particle knows when it is being observed."

Well, not the case, our methods of observation are what messes things up, not the observation itself. This experiment shows that because when we observe one of the entangled photons we still get a wave pattern.

I think this is big :)

What Goes Around Is Really Round: "Improved measurement of the shape of the electron"

drorzel — Fri, 27 May 2011 08:02:28 +0000

What Goes Around Is Really Round: "Improved measurement of the shape of the electron"

The big physics story of the week is undoubtedly the new limit on the electric dipole moment (EDM) of the electron from Ed Hinds's group at Imperial College in the UK. As this is something I wrote a long article on for Physics World, I'm pretty psyched to see this getting lots of media attention, and not just from physics outlets.

My extremely hectic end-of-term schedule and general laziness almost make me want to just point to my earlier article and have done with it. But really, it's a big story, and one I've been following for a while, so how can I pass up the chance for a ResearchBlogging post on this?

OK, you said this is about a dipole moment, but the headlines all talk about measuring the shape of an electron. What do these have to do with one another? A "dipole moment" is just a bit of mathematical apparatus used to describe a non-spherical distribution of charge. It turns out to be mathematically convenient to talk about "polar moments" of various fields in electricity and magnetism. The simplest sort of field is a "monopole," made by a point charge, which pushes other like charges directly outward from itself. Slightly more complicated than that is a "dipole" pattern, which is like what you get when you sprinkle iron filings over a magnet-- the field pushes out at one end, and pulls in at the other, and has some sideways component in between. You can make an electric dipole by putting a negative point charge close to but not exactly on top of a positive point charge.

So, an electron is made up of a little positive thing stuck to a bigger negative thing? There doesn't need to be actual positive charge present-- you can just take some of the negative charge from one pole of a spherical ball of charge and move it to the other pole. That creates a little bit of a dipole moment, too, without needing any of the opposite charge.

OK, so an electron is supposed to be like a ball of charge with a bump on one side and a divot on the other? Well, it could effectively look like that, but this measurement shows that it doesn't. Which in some ways isn't surprising, because it shouldn't be anything but round, according to the simplest models of physics.

Wait, what? These guys set out to measure something that shouldn't exist, and they're getting in all the papers for not finding it? Isn't that kind of a racket? Yes and no. The simplest models of physics tell us that the electron shouldn't have an EDM, because it would violate time-reversal symmetry.

What does making an electron lumpy have to do with time? The thing is, the electron isn't just a point charge. It also has a magnetic dipole moment, which is associated with a property called "spin," because it looks like what you would get if the electron were a spinning ball of charge (it's not literally a spinning ball, but it behaves as if it were). The magnetic dipole moment points along the axis of the spin, and the electric dipole moment, if it exists, must also point along the spin axis, in either the same direction or exactly the opposite direction.

Now, the laws of physics should be symmetric in time-- that is, if you made a movie of a simple particle's behavior, and ran it backwards, there shouldn't be any way to tell which direction the video was playing. An electron EDM violates this, though, as seen in this picture lifted from my Physics World article:

In the figure, the blue arrow represents the direction of the spin of the electron, the purplish ball of charge. If you take a little bit of charge from one pole and move it to the other, as in the second figure, you create an EDM, shown by the red arrow in the middle figure, which points in the same direction as the spin.

When you reverse the flow of time, though, as shown in the picture on the right, the blue spin arrow reverses its direction, because the electron is now "spinning" the other direction. The EDM, however, stays where it is, because reversing the spin direction doesn't affect the position of the extra lump of charge. So, the electron with time going forward has both arrows in the same direction, while with time going backwards, they point in opposite directions. This violates time-reversal symmetry.

So the electron shouldn't have an EDM, and these guys were wasting their time looking for it. Why is this news? The thing is, we know that there should be some processes in the universe that violate time-reversal symmetry. If time-reversal symmetry were never violated, then another symmetry of the universe, "CP" symmetry would never be violated, either. But if CP-symmetry wasn't violated, the Big Bang would've created equal amounts of matter and antimatter, which would've annihiliated leaving nothing but photons. Since nearly everything we see in the visible universe is matter, not antimatter, we know there must be CP-violation, which means there must also be T-violation. Thus, it should be possible for an electron to have an EDM.

So, wait, if there are time-reversal symmetry violations, does that explain the arrow of time? Do I look like Sean Carroll? Go ask him.

OK, OK, don't get touchy. So, now you're telling me that this EDM thing ought to exist, even though it shouldn't, and that's why it's big news that they didn't find it? Well, it can exist. The problem is, the Standard Model of particle physics predicts an absurdly tiny EDM, so small you could never hope to measure it.

We know that the Standard Model can't be the complete story, though, and most theories of particle physics that go beyond the Standard Model predict the existence of exotic particles that would allow a bigger electron EDM. The predictions of those models are much larger, in a range that a really clever experiment can hope to detect.

So, this experiment is looking for an EDM that would only exist if some exotic theory of physics was true? Right. The basic situation is summed up in this plot, again lifted from the Physics World article, which I got from Dave DeMille at Yale before that:

The horizontal axis here represents the size of the EDM predicted by various theories, with smaller EDM's to the right, and each line representing an order of magnitude decrease in size (it's like an astronomy plot, basically-- backwards and logarithmic). The red blob in the upper right is the Standard Model prediction, while the other colored blobs represent the possible ranges of EDM's predicted by a host of more exotic theories. The solid line represents the best experimental limit on the electron EDM, which you can see is already cutting into the theoretical predictions.

And this new paper shifts that line to the right? Exactly. It moves the experimental limit most of the way to the next tick mark.

And they did this by, what, grabbing a bunch of electrons and sticking them in an electric field? Not exactly. If you just stuck a bunch of electrons in an electric field, you would just make a particle accelerator-- they'd go whoosing off toward the positive side of your field, and not stick around to be measured.

To do this sort of measurement, you need electrons that will stick around for a while, but that experience a big electric field at the same time. The way to do that is with polar molecules.

Polar molecules? Molecules from Antarctica? No, molecules that are positive on one end, and negative on the other (very roughly speaking). If you take a really heavy atom (ytterbium, in this case), and bind it into a molecule with a really light atom (fluorine, in this case), you get a situation where the electrons inside the YbF molecule see a really big electric field. And if you apply a moderately large electric field to a sample of these molecules, you can line them all up in a way that produces a measurable shift in the energy levels of those electrons. You can measure that shift using clever techniques from atomic spectroscopy, which are explained in more detail in that Physics World article.

You're really high on that, aren't you? It's some of my best work. Anyway, the point is, you can measure exceedingly tiny shifts in the energy levels of these molecules. And the direction of the shift should depend on the direction of the electric field that you apply to the molecules. For one field direction, they shift up, while for the opposite direction of the field, they shift down.

So, you take a bunch of them, put an electric field on and measure the energy levels, then reverse the field and see what happens? In broad outline, yes. Of course, it's much more complicated than that, because there are all sorts of systematic effects that might make it look like the shift changed due to the changing field, when really it didn't. The bulk of the work for this paper, like any precision measurement paper, was in tracking down and ruling out as many of these systematic errors as possible.

Such as? They looked at things like a possible slight offset in the field, which would prevent them making a complete reversal. And a possible leakage current from the high-voltage electric fields plates slowly discharging through the rest of their vacuum system. And a possible stray magnetic field cause by induced polarization of their magnetic shields due to the transient current when they switched the electric field direction. And lots of other things.

That sounds... Kind of maddening, really. It does take a certain personality type to succeed in that business.

And after all that, they measured nothing? Yes. They measured nothing better than anybody has ever measured nothing before. Their data look deceptively simple:

Those eight points represent a total of 25 million individual measurements of the edm shift, not counting a bunch of additional checks on systematic errors. The error bars are due to the uncertainties in the individual measurements, while the solid line represents the average of all eight. The dashed lines give the uncertainty in the average, which you can see is more than big enough to include zero. Thus, the end result of all the work is that they have not detected any EDM distinguishable from zero.

That's... not as dramatic as it might be. Which is probably a big reason why they phrase the report in terms of an absurdly precise measurement of the "roundness" of the electron charge distribution. They're accentuating the positive.

So, does this answer any outstanding questions in particle physics? Not yet, no. It does make life even tougher for some moderately popular theories, though. It takes another small bite out of that theory graph up above.

But is that it? I mean, they've done their best measurement, so is it hopeless from here? Hardly. They've done a really spectacular job with this measurement, but there are some clear steps forward to the next round. They know what they need to do to reduce some of their biggest sources of systematic uncertainty, and push the limit down even farther.

There are also lots of other groups at work in this area, trying to find an electron EDM in other types of molecules-- thorium monoxide is a fun new contender-- and other systems as well. DAMOP has a whole session on precision measurements coming up in a couple of weeks, with about half of the talks having to do with EDM searches, and there are probably a slew of posters on the subject as well. It's a hot field right now.

Thanks, that was very helpful. Would you like to close this with a cheap shot at particle physicists? Not a real cheap shot, no, but I do think it's worth pointing out that these experiments explore some of the same areas of fundamental physics that you get in experiments at the LHC, with a budget 3-4 orders of magnitude smaller than the cost of the LHC. These are incredibly impressive examples of the art of experimental physics, and all these experiments fit into ordinary-size labs in physics departments all over the world.

I think these are amazing experiments that don't get enough publicity most of the time, so it's good to see them finally getting some press. And I think it would be absolutely awesome if one of the many EDM search experiments managed to scoop the LHC by either ruling out all the popular variants of supersymmetry by pushing the EDM limit down below the range they can predict, or turned up the first positive proof of some beyond-the-Standard-Model theory by finding a non-zero EDM. But then, I'm biased, because this stuff originates in my little corner of physics...

(In addition to the oft-mentioned Physics World article, there's a good ResearchBlogging write-up of this over at A Quantum of Knowledge, which I discovered when I went to ResearchBlogging to get the citation code below.)

Hudson, J., Kara, D., Smallman, I., Sauer, B., Tarbutt, M., & Hinds, E. (2011). Improved measurement of the shape of the electron Nature, 473 (7348), 493-496 DOI: 10.1038/nature10104

drorzel Fri, 05/27/2011 - 04:02

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Experiment

In the News

Physics

Precision Measurement

precision measurement

research-blogging

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Thanks for the link back! I've been a big fan of your writing for a long time!

Really nice post. In particular I agree completely with:

"I think these are amazing experiments that don't get enough publicity most of the time, so it's good to see them finally getting some press. And I think it would be absolutely awesome if one of the many EDM search experiments managed to scoop the LHC by either ruling out all the popular variants of supersymmetry by pushing the EDM limit down below the range they can predict"

thanks
Marco

Wow! That was the most compelling writing on physics I've read in as long as I can remember. Very clear and interesting explanation of a tough topic. Much appreciated.

Nice writeup.

How much an improvement is this on the previous best result?

A lot of work put into this post, thanks. Note that even though the electron could in principle have (effectively) and EDM, it is also to be considered a "point charge." To rehash some physics history: Electric field has some energy content, proportional to E^2. If you integrate the simplistic field of an electron to the "classical electron radius" you get the entire mass of the electron. Well, if you simplistically include "all the way down" to a point, you get infinite energy. (Classically, even w/o QM.) This energy must have inertia, which causes trouble if it exceeds electron mass.

The QM solution is roughly, that the e-field polarizes the vacuum of temporary virtual electron-positron pairs. This draws positrons closer to the electron etc. which makes the field near the "singularity" less intense. It's a sort of renormalization. However I still don't see how we could avoid an effective electromagnetic mass larger than m_e with this. There would have to be very much weakening of electron field in the vicinity of the CER value to have integrated field energy not overshoot (which even then wouldn't explain why the electron has the basic, "undressed" mass and charge it needs.) I'd like to see a chart that compares actual electron E field (like from e to e collisions) to the Coulomb value, at various radii from center. What integrated inertia does that produce? Maybe I'm oversimplifying or missing some angles, but it should be a legitimate start to an answer from someone. (Maybe the author could deign to start replying again ;-)

Is one of the theories really called "extended technicolor"? Or is it there just to see if anyone is paying attention?

@6 don't you own a wikipedia?

Amit:

There's also the problem with "The Axis of Evil" in cosmology. Really, I'm not joking - look it up.

electrons r not sphere shaped their like needle shaped like compass needles.ck out the works of Maurice Cotterell.mainstream particle physics is bs...

You should have made a stronger point about measuring nothing better than anyone had before. Anything that pushes the boundaries of experiment is a challenge, and at both extremes (a very crude measurement of something at high energy or a very precise measurement of nothing at low energy) you have to put most of your attention on statistics and the possible uncertainties in your measurement.

Noise or signal? Bump or fluctuation? Same problem.

Do I look like Sean Carroll?

No, he's a cat person.

Active Engagement Works: "Improved Learning in a Large-Enrollment Physics Class"

drorzel — Mon, 16 May 2011 08:31:18 +0000

Active Engagement Works: "Improved Learning in a Large-Enrollment Physics Class"

Physics is a notoriously difficult and unpopular subject, which is probably why there is a large and active Physics Education Research community within physics departments in the US. This normally generates a lot of material in the Physical Review Special Topics journal, but last week, a PER paper appeared in Science, which is unusual enough to deserve the ResearchBlogging treatment.

OK, what's this paper about? Well, with the exceptional originality that physicists bring to all things, the title pretty much says it all. They demonstrated that a different style of teaching applied to a large lecture class produced better attendance, more student engagement, and better learning as compared to a control section of the same course taught at the same time.

So, they showed that there are better methods than the traditional lecture. Haven't we known that for decades? How does that get into Science? Well, this is an exceptionally clean test, with all the sorts of controls you would want for good science. They took two sections of a huge introductory class, about 270 students each, and for a one-week period, they had one section taught by the regular professor (a highly regarded lecturer) and one section taught by a post-doc trained in a new teaching method. They covered the same material, using many of the same in-class examples and "clicker" questions, and at the end of the week gave both sections a short exam on the material just covered.

And the results were impressive? Very. The students from the experimental section got an average score of 74% on the test, compared to 41% for the control section. The two distributions were really dramatically different:

Yeah, that's a pretty dramatic difference. Are you sure they got the same test? It says that they did-- I'm not in British Columbia, so I can't confirm it. Interestingly, it notes that the experimental section only covered 11 of the 12 topics on the test due to time constraints, so they were starting with a slight handicap.

So what's the brilliant new method? Basically, making the class more participatory.

The experimental method asks the students to do most of the fact-based learning outside of class-- reading some explanatory material whose nature is unclear-- and spends the in-class time answering questions in small groups. They're posed a question, given a couple of minutes to discuss it with their partners and submit answers via the clicker system, then given some feedback on the answers. At intervals, they're given more involved "group tasks," asking them to figure out something more complicated. There are also some demonstrations, the nature of which was unclear.

You used the word "unclear" twice. Unclear, how? Well, in annoying glamour-journal fashion, they push most of the good stuff off into the "supplementary online material." this includes the twelve test questions and all the clicker questions and group tasks. It doesn't explain what demonstrations were done (though a demonstration is mentioned in the text), nor does it identify what they were supposed to read. It says "students were assigned a three- or four-page reading, and they completed a short true-false online quiz on the reading," but doesn't say whether that was reading from a textbook or something written especially for the class. I suspect it was a textbook section or so for each class, but there's no way to tell.

So, all of these gains come from doing problems in class? From having the students do problems in class, apparently. Though they're not all that involved, as problems go-- the questions were all multiple-choice, as you would expect for a 270-student class.

Can you give an example? Sure. The material covered was on Maxwell's equations and electromagnetic waves, and one of the clicker questions was:

Which of the following is true?

a) For EM waves to exist, they must propagate in a medium with atoms. With no
atoms present, the field cannot have any effect on the system and therefore can't
exist.

b) An EM wave can propagate through a vacuum.

c) An EM wave is like a wave travelling along a rope in that it needs atoms to move
up and down.

d) An EM wave can only propagate in a vacuum since any medium would get in the
way of its propagation.

e) More than one of the above is true.

They would get this, discuss with a partner for a few minutes, enter their answers, and then the instructor would give feedback to the class.

OK, so that's a clicker question. What's a group task look like? From the same lecture, we have:

A friend of yours reminds you that en EM wave consists of both an E and B field.

She asks you if the following electric field

E(x,t)=100x²t Volts/m

could be that of an EM wave.Can you help? Be quantitative in your answer.

That's a little subtle. That's the idea. They would get a longer time to work these out, with some feedback along the way.

So, the whole class is just this stuff? That's the idea, yes. The control group was a more traditional sort of lecture, though it used "clicker questions" as well.

It seems kind of surprising that this would lead to such a big improvement. Are you sure that this isn't some other effect? A more enthusiastic instructor, or some such? While the instructors for the experimental section were authors on the paper, and thus presumably deeply committed to the project, they're also post-docs with minimal prior teaching experience. While it's hard to rule out an instructor effect, it's unlikely to be just that.

Could this just be an effect of novelty? You know, anything you do to liven the class up improves performance? The technical name for the "any change you make improves things" is the "Hawthorne Effect," after an experiment around 1930. They vehemently deny that this is what's going on, citing a number of sources claiming the effect doesn't really exist (including this old paper from Science, which is several kinds of appalling. Interestingly, though, they sort of implicitly claim a Hawthorne-ish effect to explain one of their results, namely the vastly improved attendance in the experimental section, which rose from 57% the weeks before the trial to 75% during the experiment. They suggest that the novelty of the trial got students to come see what was happening, and the new methods got them to stay. Make of that what you will.

So, what are the limitations of this? Well, basically, it was a one-week test of a new and different method of teaching, followed immediately by a short test that was basically identical to some of the in-class material used during the experiment. It doesn't tell you whether the effects would hold up for a full semester (though previous studies have compared entire courses taught with new methods, and suggest substantial gains), or how well the material would be retained. It would've been interesting, for example, to see if the experimental section scored substantially better on final exam questions covering the material from this part of the course.

That's a good point. I wonder why they didn't do that? Probably because it would've complicated what was otherwise a very clean test. Also, I suspect either logistical (sorting out the relevant questions from the final) or ethical (there might be trouble getting permission to use student test scores as part of a research paper, unlike using a voluntary separate assessment that did not affect the final grade) issues may have come into play. They don't mention it at all, though.

Anyway, it looks pretty impressive. Are you going to implement this? It's a fairly compelling argument in favor of their methods, but I'm not sure. The "get them to read the book ahead of time" thing is problematic at best, and our more compressed schedule makes it harder to do more time-intensive methods of instruction (their experiment ran in week 12 of a semester; our entire course has to fit a 10-week trimester). Also, there's the problem of being the one person trying a new technique (I got killed on my student evaluations last term because I did a couple of things differently than the colleagues teaching the other sections), and the fact that the supplementary material includes the sentence: "We estimate that under normal circumstances a moderately experienced instructor would require about 5hrs of preparation time per one hour class in this format." That's a little daunting.

It's definitely something I'll think about for the fall, though, as I'll be the only person teaching intro mechanics that term, giving me a little more flexibility in terms of how I run the course.

Deslauriers, L., Schelew, E., & Wieman, C. (2011). Improved Learning in a Large-Enrollment Physics Class Science, 332 (6031), 862-864 DOI: 10.1126/science.1201783

drorzel Mon, 05/16/2011 - 04:31

Tags

physics education research

As far as evaluations go- it may be worth remembering that the majority of the students said they wished the whole course had been delivered like that.

As a random aside... the traditionally taught students produced a lovely bell curve of results on the multiple choice test (that was probably developed to give such a lovely bell curve in such students).
If you taught everyone with the new method, and you wanted to maintain a bell curve result, you'd have to change the test (in most of the 260 person classes I've taken, there is a general attitude that a test producing bell-shaped curves is more valid than others, so that valid statistical assumptions are easier, I presume)
So it's important to remember that the students probably won't notice they are learning more with this method if they are all exposed to it and you adjust the exam as well.

Wow, 57% attendance is pretty awful. I went to a big state school as an undergrad, but I don't recall attendance being so low in my large introductory physics classes. Did the paper mention what fraction showed up for the traditional lecture during the trial?

So it's important to remember that the students probably won't notice they are learning more with this method if they are all exposed to it and you adjust the exam as well.

Yeah.
That's why I didn't mention the student opinion questions in the write-up. I tend to discount those results because of the novelty factor-- the one week where they did something radically different was probably the most interesting week of the term precisely because they did something radically different. If the whole term was taught that way, though, the novelty factor wouldn't be there, and they might find just as many things to complain about as in the traditional format.

Did the paper mention what fraction showed up for the traditional lecture during the trial?

Control section attendance was 55% pre-experiment and 53% during. The table caption says this is the "Average value of multiple measurements carried out in a 2-week interval before the experiment." There's a comment somewhere in the text that suggests there may have been students going in and out to some degree (showing up to turn in/ collect homework, then leaving, or rolling in significantly late, etc.).

The "get them to read the book ahead of time" thing is problematic at best, and our more compressed schedule makes it harder to do more time-intensive methods of instruction (their experiment ran in week 12 of a semester; our entire course has to fit a 10-week trimester).

You mean that students will do better on a standardized test if they actually (like I imagine every teacher tells them to do at the beginning of the semester) read the material before coming to class?

Say it ain't so, Joe!

I don't think you can make a comparison between traditional and "new" methods until you isolate this very important variable and the extent of its effect first. Unless possibly you could make the case that the nontraditional method in and of itself encourages proper behaviour.

Regarding both attendance levels and reading the material...

Was the test at the end of the week part of their course grade? If not, that might explain much.

It sounds like the difference between the two methods is the amount of time students spent outside of class on the material. In large lecture classes, I usually took notes and then ignored the material until it was time to study for the test or do homework. Here it sounds like the students were evaluated on their readings *every day* (the short on-line quiz) and then had to perform in class. The daily assessment might be the important part, rather than the in-class work.

In my own teaching, I've found that the more often I quiz, the better students do. Being graded seems to be the strongest student motivator.

Is there a way to avoid 250+ student classes anymore? (She asks as a parent of a high school sophomore looking at colleges...)

This is tangential, but to simply improve class attendance, I found that having unannounced quizzes on the previous day's material worked wonders. My attendance in chemistry survey and organic chemistry was usually around 90% or better, much better than the 50% attendance otherwise seen. I also liked to include occasional challenging questions in my "lectures," but unfortunately my students almost invariably got annoyed and frustrated in those situations.

We've tried clickers in a second-year statistics class, without the rest of the package, and got similarly impressive increases in attendance, and some improvement in performance on the final exam. We didn't find any clear benefit (or harm) from the pre-reading and group tasks, in a different class, although the students liked it. We only had historical controls, not parallel controls, though.

In our context worried not so much about a Hawthorne effect as a Red Queen effect. The students liked the clickers, which may well explain the increase in attendance, and the increase in attendance could easily explain the exam differences. The effect may wear off as clickers become familiar and boring. A related possibility is an arms race: we're competing against other courses for student attention, and the novelty makes students spend more of their effort on this course. If everyone did it, the benefits might go away. The duration of the benefit is important because reorganising a course this way takes quite a lot of work, which you'd want to amortize over several years.

@ScentOfViolets: Unless possibly you could make the case that the nontraditional method in and of itself encourages proper behaviour. Well, yes. That's exactly the case they are trying to make. The argument is that not presenting material in lectures encourages reading it, and that doing problems in lectures encourages concentration on the problems, and that these are both important behaviours. Having the material explained in lectures and having students read the material in advance would presumably be even better, if you had a strategy that could make it happen.

Of course attendance and reading have a significant effect, and one benefit of innovative approaches (I classify this as one of many forms of active engagement) is an improvement in both. However, reading the book only works if the book is actually meant to be read. That is why I also wonder what text those students were reading.

To Sherri @7:
You can avoid those colleges by asking that question. You might, for example, be able to use on-line registration tools to see what the class sizes are for relevant courses AND who is teaching them.

It should increase both reading the material and working on problems which many students ignore and don't realize they don't understand something until confronted with not knowing how to apply it. The groups could help both by lesser students gathering how to use the concepts and better students learning by how to explain themselves.

Was the test at the end of the week part of their course grade? If not, that might explain much.

No. The test whose scores are plotted in the graph above was part of the study, but not included in the final average. At least, that's how I read it.

Is there a way to avoid 250+ student classes anymore?

At the risk of sounding self-serving: Small liberal arts colleges. It doesn't completely eliminate large lectures-- I know of a few classes that fill a big auditorium for the weekly lectures-- but most of our classes are smaller, and in Physics, our intro course is taught in sections that are capped at 18 (but lots of sections).

Chemistry has had http://www.pogil.org/ since the 1990's.

I know someone who implemented POGIL in community college organic chemistry. According to him, the students did amazingly well on the ACS national test and it was a pleasure to teach because the students were engaged in learning in the classroom. It's not simply a matter of adding clickers and a few group exercises -- there is a lot more to making the technique effective, hence the term "guided inquiry". But at the time, the big 4-year Tier I research University refused to even try this teaching method.....

I think I would kill to have more classes that involve actual engagement like this.

Is there a way to avoid 250+ student classes anymore? (She asks as a parent of a high school sophomore looking at colleges...)

I second Prof. Orzel's recommendation of small liberal arts colleges. I think my largest class size so far has been 30 or so with the average close to 20. I just finished one that had 9 or 10 students in it.

I chortled when I read the description of the "new" teaching approach. I've taught the didactic component of a junior-level course in the discipline I teach (nursing) using problem-based learning since 2007. Yes, the students hated it. Yes, it means they have to read the textbook. Yes, my evaluations were kinda sucky there for a while.

On the other hand-- mean scores on a nationally standardized test of the content I teach have gone up every semester and are consistently higher for my content area than for the other content areas tested on the same cohorts of students in the same semesters.

It did require a significant investment of time from me to adapt all my lectures to case studies that would incorporate the same content, but it's been worthwhile. My textbook is going to a new edition this year and we've started enrolling slightly larger cohorts, which means I'll have to revise everything about the course this summer. That's the job, right?

Did you notice how much multi-tasking occurs during the course of their new methodology? It has been demonstrated that multi-tasking has long-term negative consequences, so what are the potential long-term negative consequences of this new study?

The control group was crap. An appropriate control group would have been to take a class taught in the new method from the beginning (which they say they have at this school) and convert it to standard lecture format in parallel with the experimental conversion of a normally taught class to the new methodology.

No comments were made on students who dropped out of or did poorly in the new-method, and whether these students would have likely dropped or done poorly in conventional lecture courses. Given pre-experiment and post-experiment quizzes, as well as the existence of entire courses taught with the new methodology, there's no excuse for this lack. These studies need to be done before studies like the current one are lauded. The unforeseen negative effects of these avant-garde teaching (I almost wrote "learning") strategies need to be discovered and addressed.

I submitted an e-letter to this paper which was declined by Science that covers even more points (such as the study they reference to dismiss the Hawthorne effect explicitly stating it is not applicable to the kind of study performed here). They never responded to my points.

I speak as a person who has been an undergraduate for about 9 years (cumulative) over the last 16 years. I speak as a person who prefers minimal group studying and maximal individual or one-on-one studying (and prefers the use of resource centers where such one-on-one studying can take place over any group-based study). I hate group-based study, yet it's been made all the rage in the last twenty years. Please don't continue to mess people like me over in the name of what's good for the majority. There is plenty of room for the educational diversity that can address everyone's needs, but too often the new-wave makes a clean sweep of everything (Charles Eliot, papers instead of textbooks, PLTL to the exclusion of tutoring, etc...).

Robert Evans

is it possible that the "experimental" section taught the test ?

At my University, the Administration is highly supportive of these kinds of approaches -- and they seem to be very aware that one result of the implementation will be negative student evaluations. They have let us know in advance that they are expecting negative student evaluations, and the retention/tenure/promotion for faculty using engagement methods are not going to punish faculty for these evaluations. I think administrators wanting to encourage these innovations NEED to be aware of this if they want faculty to try more active approaches.

Bouncing Neutrons for Fun and Science: "Realization of a gravity-resonance-spectroscopy technique"

drorzel — Thu, 21 Apr 2011 08:17:06 +0000

Bouncing Neutrons for Fun and Science: "Realization of a gravity-resonance-spectroscopy technique"

Several people blogged about a new measurement of gravitational states of neutrons done by physicists using ultracold neutrons from the Institut Laue-Langevin in France. I had to resort to Twitter to get access to the paper (we don't get Nature Physics here, and it's way faster than Inter-Library Loan), but this is a nice topic for a ResearchBlogging post, in the now-standard Q&A form:

OK, why was this worth begging people on Twitter to send you a copy? The paper is a demonstration of a sort of spectroscopy of neutrons bouncing in a gravitational field. They showed they could drive neutrons bouncing on a "mirror" between two of the discrete quantum states of the system, and measure the energy difference between those states very accurately.

Wait, neutrons bouncing on a mirror have discrete states? Why doesn't anybody tell me these things? Well, you didn't ask. Anyway, yes, neutrons bouncing on a mirror have discrete states, just like any other quantum system. Quantum mechanics tells us that confined systems will always exist only in special discrete states-- that's what puts the "quantum" in "quantum mechanics," after all.

But how are these confined? They're confined by gravity. To do the experiments, they send a beam of extremely slow-moving neutrons above a polished glass surface. When the neutrons fall under the influence of gravity, they hit the surface and bounce back upward. On the high side, the neutrons have only a limited amount of energy, and once all the kinetic energy of their vertical motion has been turned into gravitational potential energy, they turn around and fall back down, just like a tennis ball thrown up into the air for a dog to chase after.

Yeah, but tennis balls don't have discrete states. They do, you just can't tell the difference between them very easily, because they're so close together in energy, and the wavelength is so small. A sample of slow-moving neutrons, though, can clearly show these different states, which are described by wavefunctions that look like this:

The solid lines show the probability of finding the neutron at a given height (probability increasing to the left) for the first four states of a neutron bouncing on their mirror. It's taken from an older paper (from 2002) where they demonstrated the existence of these quantized states.

How did they do that? The basic technique is the same one they used for the detection in this experiment: they put an absorber above their mirror at a set height, to block any neutrons in states that extended up too high.

You can see from that figure that as you go up from one state to the next, the probability of finding the neutron at higher elevations increases. Neutrons in the lowest state will basically never be found more than 20 microns above the surface, while neutrons in the third state (from the left) have a pretty good probability of turning up that high.

So, how does an absorber help demonstrate the existence of these states? I mean, as you move it closer to the mirror, it'll block the higher states, but you expect the number making it through to decrease anyway, because there's less space to squeeze through. Right, but in a classical system, no matter how narrow you make the gap, some neutrons can always sneak through. In a quantum system, if the gap is too small, the neutrons will always be absorbed, so there should be a minimum height below which nothing makes it through.

And that's what they saw? Yep. It looked like this:

The solid line is the classical prediction, the points are the data for various heights of the absorber. You can clearly see the cut-off: below about 15 microns, nothing makes it through, even though classically there should be some transmission.

OK, so you can see the lowest-energy state. So, for the current paper, they did what, raised the absorber higher and looked for steps in the transmission? Better than that. They demonstrated a way to drive the neutrons from one state to another by shaking the mirror on the bottom. They picked out the lowest-energy state with a narrow mirror-absorber gap in the first stage of their apparatus, then used a vibrating mirror to put the neutrons into the third energy state.

So, instead of pushing the absorber down, they brought the bottom mirror up? No, they used the shaking on the mirror to pump energy into the system, and resonantly transfer the neutrons from the lowest energy state to the third state. When they shake the bottom mirror at exactly the right frequency, the neutrons pick up energy from the shaking, and move to the third state; at frequencies a little higher or lower, they just stay in the lowest energy state where they were all along.

Wait, how does that work? Well, you can think of it as being a little bit like when I take SteelyKid to the playground, and put her on the swings. If I push the swing at just the right rate-- basically, once per swing, as she comes back to where I'm standing-- she quickly starts swinging higher and higher (and yelling "Faster!" and giggling). If I were to push at a frequency a little higher or lower, I would sometimes increase her swing, but a few swings later, I'd be pushing her before she got to the end of her oscillation, and that would interrupt her swinging and bring her to a stop.

And she wouldn't like that. No. Not one little bit. That ideal frequency of pushing for a swing is set by the length of the chains on the swing, which determine the time needed for it to go through one full oscillations.

In the case of the bouncing neutron, the ideal frequency of pushing is set by the energy difference between states. If they shake their bottom mirror up and down at a frequency equal to the energy difference between the first and third states divided by Planck's constant h, they will take atoms from the lowest energy state and move them to the third energy state.

Wait, why the third state? Don't they have to go through the second state? No, because quantum states are discrete and independent. You can go directly from state 1 to state 3 or state 5 or state 137, without passing through the intervening states, so long as the frequency of the shaking is at the right frequency.

The probability of making that transition goes down as you go to higher states, because higher states spend most of their time at higher elevations than the lowest energy state can possibly reach, so it's not that easy to go directly from a low to a high state. There's no fundamental reason why you can't go directly to any state you like, though.

So why did they pick state 3? I don't know. Probably because it gives a cleaner separation between the neutrons remaining in state 1 and those moved to state 3, since the maximum height difference is greater.

OK, so, let me see if I've got this: they send neutrons in, use an absorber to pick out only the lowest energy state, then use a shaking mirror to excite those neutrons to the third energy state. Then, what, they stick in another absorber and look at what makes it through? You've got it exactly. They use a third mirror section with an absorber placed at a height that picks out and blocks the third state, and they show a decrease in the number of neutrons making it through.

Shouldn't you show a graph at this point? Sure:

The top figure shows the transmission of neutrons through the absorber region as a function of the frequency of the shaking. The dip corresponds to two different amplitudes of the moving mirror, showing that you get more neutrons making the transition when you shake a little bit harder. The second graph is a combination of all their measurements into a single plot, with the horizontal axis being a sort of fractional difference between the frequency of the shaking and the resonant frequency.

Yeah, that looks like a clear dip, doesn't it? Yep. It's a pretty nice, clean signal, showing that they have some control over the states of their system. It's be nice if they could show Rabi oscillations clearly (that is, demonstrate the ability to drive the neutrons from state 1 to state 3 and then back to state 1), but given what they're working with, it's a little amazing they can do this at all.

OK, this is cool and all, but what is this good for? Well, the spacing between the states depends on the gravitational attraction between the neutrons and the Earth, so probing the difference between these states tells you something about gravity and the acceleration of gravity. This can be a test of the equivalence principle saying that the inertial mass in Newton's Second Law is the same as the gravitational mass, which is the cornerstone of general relativity.

The scale over which these things move is really small-- 10-20 microns-- so this might also provide a way to test the behavior of gravity on those kinds of separations. Since neutrons are, by definition, neutral, they're not strongly effected by electric charges and things like that, making them potentially a very good tool for testing theories that predict a dramatic strengthening of gravity at small distances.

There's a lot of cool fundamental physics stuff you can imagine doing with a system of slow bouncing neutrons. This paper demonstrates some ability to manipulate the states of these neutrons, which is one of the key prerequisites to doing any of the really cool stuff.

And, you have to admit, it's pretty cool in its own right.

Jenke, T., Geltenbort, P., Lemmel, H., & Abele, H. (2011). Realization of a gravity-resonance-spectroscopy technique Nature Physics DOI: 10.1038/nphys1970

Nesvizhevsky, V., BÃ¶rner, H., Petukhov, A., Abele, H., BaeÃler, S., RueÃ, F., StÃ¶ferle, T., Westphal, A., Gagarski, A., Petrov, G., & Strelkov, A. (2002). Quantum states of neutrons in the Earth's gravitational field Nature, 415 (6869), 297-299 DOI: 10.1038/415297a

drorzel Thu, 04/21/2011 - 04:17

Tags

Thank you. I love these very clear explications.

I recall reading about the proof of concept years ago after my own visit to the ILL.

1) Obligatory snark: If you talk about this out loud, a particle physicist will hear that someone was observing particles on a PeV energy scale and have a heart attack.

2) The "Don't they have to go through the second state?" question offers a perfect opportunity to point out that there are no quantum jumps in the sense Bohr used the term. Notice that there is a reasonable probability for a particle to be at about 5 (mu)m about the mirror in ANY of those states. It doesn't have to jump to a different place to change its energy, it picks up energy at that place ... just like SteelyKid getting pushed on the swing at a particular place.

3) I love the scale invariance of certain constants. For example, hc = 1240 eV*nm (for atomic physics) becomes 1240 MeV*fm in nuclear physics and meV*(mu)m for condensed matter. Here we are using hc = 1240 peV*km, so those neutrons have a REALLY long wavelength.

So by "potentially a very good tool for testing theories that predict a dramatic strengthening of gravity at small distances." I assume you mean measuring the cutoff distance for the resonance one bounce, and how it varies based on the mirror composition?
Say, a mirror made of ice vs mirror made of lead.
Or a mirror over a vacuum vs mirror over a lead block

So, are we seeing quantized kinetic energy or quantized gravity here?

I don't know how much variability there can be in the construction of the mirror and absorber. I think the mirror needs to be prepared pretty carefully, so I don't know how much that can be changed.

I'm mostly just relaying claims made in the introduction of the paper, but I think the basic idea is that if there is any substantial strengthening of gravity at short distances, that would show up as a small shift in the energies of the states of the neutrons due to the extra gravitational attraction of the mirror (and to a lesser extent the absorber. The gravitational interaction between the neutrons and the mirror will be small, but the distance between them is only 10 microns or so, so the energy associated with the interaction might be significant when compared to the gravitational potential energy associated with a 10 micron change of altitude near the Earth's surface. You would presumably look for an energy shift that affected the low-energy states (which spend most of their time near the mirror) more than the high-energy states. So, for example, the energy difference between state 1 and state 2 would be significantly bigger than expected, while the difference between state 2 and state 3 would be only a little bigger than expected, and the difference between state 3 and state 4 would be even closer to the expected value, and so on.

That's a guess, though, based on a couple of minutes of thought. There might be a more elegant way to get at this.

So, are we seeing quantized kinetic energy or quantized gravity here?

Quantized energy of motion of the atoms, which is to say both kinetic energy and gravitational potential energy. This is not quantum gravity in any meaningful sense of the word (unless something wacky happens at short distances, in which case you might get something new). At least in the current experiments, gravity is treated as a static background field.

Could this technique be used to refine the poorly-known value of big G?

Neutrons can bounce off of solid surface? When they do, do they do mechanical work on the surface? That seems like a much better way to get work out of nuclear reactors than thermal extraction. Why isn't anyone doing this?

This is not quantized gravity in that there's been no quantization of the gravitational field.

However, it is quantized states where gravity is supplying the potential, so in a sense it's an interaction between (Newtonian) gravity in quantum mechanics. Has that been done before this paper? The vast majority of quantum experiments are done using the electromagnetic force to define the potential.

Interference of Independent Photon Beams: The Pfleegor-Mandel Experiment

drorzel — Fri, 19 Nov 2010 09:38:04 +0000

Interference of Independent Photon Beams: The Pfleegor-Mandel Experiment

Earlier this week, I talked about the technical requirements for taking a picture of an interference pattern from two independent lasers, and mentioned in passing that a 1967 experiment by Pfleegor and Mandel had already shown the interference effect. Their experiment was clever enough to deserve the ResearchBlogging Q&A treatment, though, so here we go:

OK, so why is this really old experiment worth talking about? What did they do? They demonstrated interference between two completely independent lasers, showing that when they overlapped the beams, the overlap region contained a pattern of bright and dark spots characteristic of interference.

How did they do that in 1967? What did they use, photographic plates? No, they used photomultiplier tubes, that produce an electrical pulse when a single photon falls on them.

But a PMT only detects photons in a single position. How did they make a picture out of that? They didn't, because they found a clever way to arrange it so they didn't need to. Here's a schematic of their apparatus:

All right, what are we looking at? In the upper left, you see a diagram showing the optical layout. They start with two independent lasers, and split off a small part of the light from each to go to a detector that monitors the frequency difference between the two lasers, and only turns on the detector system when the lasers are close enough in frequency to produce a good interference pattern.

Wait a minute. These are lasers, aren't they a single frequency? They are, but the frequency wanders around a little bit, just enough to change the interference pattern a little. As a precaution, they only look for the pattern at times when both lasers have wandered into the same basic range.

OK, so they've got two lasers. Then what? Then they take the two independent lasers and steer them together with mirrors, and overlap them with a small angle between the two. This should produce an interference pattern with a spacing between bright and dark fringes that depends on the angle between the beams. They put this pattern onto a specially made detector.

Yeah, that's the whole question. How does that work, when they just have PMT's as detectors? The detector they used (inspired by a Dr. Neil Isenor, who gets a footnote of thanks but not an author credit) is shown in the inset at the lower right. It's an array of small glass plates, cut like little prisms, with a thickness equal to roughly half of the spacing between one bright spot and the next in the expected interference pattern. The odd-numbered prisms-- first, third, fifth, etc.-- direct light falling on them to one PMT, while the even-numbered prisms-- second, fourth, sixth, etc.-- direct light hitting them to another PMT. When the light falls on the stack in just the right way, the bright spots in the pattern will fall on the odd-numbered prisms while the dark spots fall on the even-numbered prisms, so one detector will detect lots of photons, while the other sees almost nothing.

Yeah, but how do they get the pattern to line up? I mean, you said that the problem with this measurement is that the pattern changes position randomly all the time. That's the really clever part. They don't need to have a stable interference pattern, and they don't need to have the pattern line up precisely with one set of prisms. All they have to do is look at correlations between the detector signals.

You see, if the pattern falls with the bright spots on one set of prisms, one detector will get all the photons, while the other gets none. If you shift the pattern so the bright spots are on the other set, then the second detector gets all the light, and the first one gets none. Which shows that the signals from the two detectors should be anti-correlated-- when one gets a lot of light, the other gets very little.

But if you shift the pattern only halfway, then they each get half of the photons. True, but that's only true in a tiny range. Most of the time, one detector will get more photons than the other. That means that, statistically, you expect that any smallish sample of the count data will show a significant imbalance between the two. That's the thing they look for in the data.

And that worked? Yes. They have a table in the paper showing the counts on each detector for 25 different trials lasting 20 microseconds each. The average number of counts per detector over the whole sample was pretty close-- 5.08 for one and 4.40 for the other-- but the individual trials almost all show a significantly greater number on one detector than the other. The correlation coefficient between the two count rates is negative, as you would expect from an interference pattern falling on the detector.

I don't know, dude. It's not science without graphs. Isn't there a graph you could show? Ask, and ye shall receive:

This shows the correlation coefficient (plotted with negative numbers being up) as a function of the ratio of the thickness of the prisms L to the expected fringe spacing l. When the thickness is equal to the spacing, so that if one bright spot falls on an odd-numbered prism, the next bright spot will fall on the next odd-numbered prism, they see a maximum in the negative correlation, which drops off as the fringes get either closer together or farther apart. The lines in the graph are the predictions of a simple model of the expected statistics, for different values of the number of pairs of prisms illuminated. Their data agree very nicely with something between 2 and 3 pairs illuminated.

OK, so their detector shows an interference pattern between photons from two different lasers. How does that work, exactly? Do the two photons bounce off each other, or something? That's the other cool thing about this experiment. Before they sent the beams onto the detectors, they used big filters to knock the intensity way down. They used big enough filters that there was only one photon (on average) in the apparatus at any given time. They got around 10 photons per 20 microsecond data run, which gives an average spacing between photons of 2 microseconds, which corresponds to a spatial separation of about 2000 feet (the speed of light being very nearly one foot per nanosecond).

This large spacing means that this isn't an interference caused by two simultaneously arriving photons, but rather a single photon arriving and somehow knowing that it needs to form an interference pattern, even though it can only have come from one laser.

OK, that's just weird. How do you explain that? The key issue here is that you have no way of knowing for sure which laser the photon came from. That's what allows you to see interference. When they block one laser or the other, so that they know for sure which laser the photon came from, the interference goes away.

Yeah, but what's interfering? I mean, a photon can't really come from two places at once, can it? That's the tricky bit. They have a wonderfully deadpan way of putting this: "In terms of photons, the experiment raises one or two interesting questions of interpretation."

That's an understatement. Exactly.

There are two ways you can go with this. One is to view it as an interference created by the detection process. That's the language they use: "It seems better to associate the interference with the detection process itself, in the sense that the localization of a photon at the detector makes it intrinsically uncertain from which of the two sources it came." This is a little toward the Copenhagen side of things, interpretation-wise, though it could also be a little Bohmian. It says that the observed pattern is something to do with the detectors-- that configuring the detectors the way they did creates a situation in which the only possible outcome is an interference pattern.

Another way of putting it would be to use the language of field theory. That is, the photons we talk about as particles are really excitations of a mode of the electromagnetic field having a specific wavelength and direction. The interference pattern you see is an interference between two modes of the field, meaning that one photon coming in to the detector is necessarily an excitation of a field mode that contains the interference pattern within it.

In either case, the important thing here is that the photons are not strictly particles in the classical sense. There's something nonlocal about them, that allows an interference pattern to be produced even when you have only one photon, but aren't certain of its place of origin.

That's, um, really odd. Yes, yes it is. Which is why this experiment didn't go in the book-- it's a little too strange and requires a little too much hand-waving to explain. But it's a very cool experiment, and an impressive display of ingenuity.

Pfleegor, R., & Mandel, L. (1967). Interference of Independent Photon Beams Physical Review, 159 (5), 1084-1088 DOI: 10.1103/PhysRev.159.1084

drorzel Fri, 11/19/2010 - 04:38

Tags

* brain explodes *

Very cool man. Keep on blogging great stuff like this!

Yes, what Ted said. And, what Andrew said too.
Still, if you accept Young's Double slit experiment with single photons - and you have to , because that's what happens - then this is perfectly logical. Sometimes you have to accept what happens, without knowing the how or why.

Brad

So, the multiverse concept has new universes branching out from each quantum decision. In the case of two possible sources for the photon could this represent a merging of two universes?

In a double slit experiment I can sort of accept that you wave your hands and say the particle 'takes both ways'. And if you accept that I can accept that the amplitude is calculated as the sum of amplitudes for going through either slit.

In this two-laser case, 'taking both ways' seems harder to accept. How is the prob. amplitude calculated in this case?

(confused)

Excellent post.

I'm speculating that the wave from the laser is in a sense in effect even when there is momentarily no particle there, thus conveying to the actual particle that there is something there to interact with.
Which may be utter nonsense. I am not a particle physicist, I just like reading about it.

It's like the first time a friend explained how a correlation spectrometer worked. My reaction was, "That makes no sense at all." "Welcome to quantum mechanics."

Really nice commentary, especially the penultimate two paragraphs which summarize the position in language of QFT. Personally, I think it is time that introductory textbooks stopped distinguishing between so-called 'quasi-particles', like phonons and excitons, and 'real' particles which all occur as (fairly localised) excitations of some quantum field. Why is it that people are happy to accept creation, annihilation and non-local scattering processes for particles arising as quantised lattice vibrations but have a problem accepting essentially the same behaviour for electrons or photons? Is it really any more odd than the behaviour predicted by classical mechanics? It's just what happens, and we should get used to it.

Ok I've got a question because I still don't completely understand the setup. How is this any different from a single light source, two slits, and when you place a detector one one slit the interference pattern weakens? Basically, I'm asking, is the laser prevented from shining through the other slit? Because if that is true then it is super cool.

And one more question - so is the end result a interference pattern of two single slit patterns added on top of each other? Or a double slit pattern? Or something else? (or is there any difference? Sorry, I'm not good enough to understand the graph:P)

Indirect Excitation Control: Ultrafast Quantum Gates for Single Atomic Qubits

drorzel — Mon, 30 Aug 2010 09:49:53 +0000

Indirect Excitation Control: Ultrafast Quantum Gates for Single Atomic Qubits

Last week, John Baez posted a report on a seminar by Dzimitry Matsukevich on ion trap quantum information issues. In the middle of this, he writes:

Once our molecular ions are cold, how can we get them into specific desired states? Use a mode locked pulsed laser to drive stimulated Raman transitions.

Huh? As far as I can tell, this means "blast our molecular ion with an extremely brief pulse of light: it can then absorb a photon and emit a photon of a different energy, while itself jumping to a state of higher or lower energy."

I saw this, and said "Hey, that's a good topic for a blog post." And on Friday, the new issue of Physical Review Letters included a new paper on just this topic (arxiv version for those without subscription access), making it a good topic for a ResearchBlogging post. So,

So, what's this all about? The paper reports on a new way of moving atoms from one state to another much faster than is possible with more typical methods. This is potentially useful for speeding up the operation of a quantum computer.

Transition speeds are critically important for quantum computing, because all quantum information processing systems are subject to some interactions with the environment that will eventually destroy the quantum character of the information through the process known as "decoherence." If you do a really good job, you can get decoherence times that are measured in seconds, which sets an upper limit on the number of operations you can do with a simple system before decoherence kills you (you can do quantum error correction to extend that, but then things start to get complicated). If you can do your state-change operations in 50 picoseconds rather than tens or hundred of microseconds, you can pack a lot more computing into that same amount of time.

And this works by making atoms absorb photons and then emit them? Right. The sort of transition they use to do these operations is called a "Raman transition" after the Indian physicist and Nobel laureate C. V. Raman who worked out some of the quantum properties of the interaction between light and atoms. A Raman transition makes use of the fact that there are three different ways for atoms to interact with photons and change states.

There are? Yes, there are. An atom in a low-energy state can absorb a photon of the appropriate energy, and use that energy to move to a higher energy state, which is just called "absorption." An atom placed in a high-energy state will eventually drop down to a lower energy of its own accord, in the process of "spontaneous emission." And an atom in a high energy state that encounters a photon of the appropriate energy can be induced to emit a second photon of the same energy, and drop down to a lower energy level. This last process is called "Stimulated Emission," and accounts for the "SE" in the word "laser", which started life as an acronym for "Light Amplification by Stimulated Emission of Radiation."

Isn't that kind of weird? Not really. It seems less obvious than the others to the casual observer, but it's actually very easy to explain mathematically. You get stimulated emission very naturally from even a semi-classical model of light and atoms. Spontaneous emission is the difficult one to explain, though that's a topic for another post.

OK, so these Raman transitions, what are they? The specific case of interest is a "stimulated Raman transition," which is a subset of Raman transitions in general, as illustrated in this figure:

Horizontal lines indicate different states of an atom or molecule, with the energy increasing as you move up. The vertical lines indicate absorption or emission of photons. A Raman transition is one in which the atom absorbs a photon of one energy, and emits a photon of another energy, ending up in a different low-energy state than it started in.

A stimulated Raman transition is one where the downward step takes place through stimulated emission-- that is, after the atom has absorbed one photon, a second photon of a slightly different frequency comes along and stimulates it to emit an identical photon, and move down to a lower energy state. You can end up in a higher state than you started by absorbing a photon of one energy, and emitting a slightly lower energy, or you can end up in a lower energy state by absorbing at one energy, and emitting at slightly higher energy. These are called "Stokes" and "anti-Stokes" processes for historical reasons that don't really matter.

So you excite the atoms with one pulse of light, then send in a second pulse of light, and knock them back down? That's the basic idea. It's a little more complicated than that, though, because if you do it right, you never put the atoms in the excited state-- they go up, and immediately come back down. That's why the upper states are labeled "Virtual Energy States" in the figure-- you detune the lasers so they don't quite have enough energy to reach the excited state, but the two photons connect to the same "virtual" state at a lower energy.

You can do that? It lowers the rate at which the process happens quite a bit, but you can compensate for it by cranking up the intensity. If you use a strong enough light pulse, and a big enough detuning, you can move all the atoms from one low-energy state to another without ever occupying the excited state.

And you do this, why? Because if the atoms are ever in the excited state, there's a probability that they can decay spontaneously, which is disastrous if you're trying to do quantum information processing, because you have no control over where the atoms ends up in spontaneous decay.

No, I mean, why not just go directly from one low-energy state to the other? Why mess around with the upper state at all? Ah. The answer there is speed. It's much faster to use a Raman transition in the visible or ultraviolet than to do any kind of direct excitation.

Why is that? Well, a couple of reasons. First of all, depending on the low-energy states you're using, the transition may be "forbidden" by one rule or another-- it might require a change in the angular momentum or other properties that can't be managed with simple absorption. This means you need either really massive amounts of power, or a long time to move from one to the other.

Another reason is that the absorption process necessarily requires a time that is longer than the time for the light associated with the transition to oscillate. If you're dealing with low-energy states like hyperfine ground states, these frequencies are in the radio frequency range, which limits you to transition times in the microseconds or many nanoseconds range. Optical frequencies are something like six orders of magnitude faster, which would let you do transitions in picoseconds.

Which is what they do here? Exactly. They take a trapped Ytterbium ion, and blast it with a picosecond pulse from a laser tuned near the transition frequency between the ground state and one of the excited states. When they arrange the frequency and polarization properly (splitting the pulse in two, and rotating the polarization of one before sending it onto the ion), they can transfer the atom from one ground state to the other (separated by 12 GHz) with a single 50 ps pulse.

That's pretty fast. Yes, yes it is. Of course, this doesn't mean you'll be building a 20 GHz quantum computer any time soon-- there's a lot of other stuff that goes into a quantum computer that would require some additional time-- but this shows that, in principle at least, you can do the necessary state changes extremely quickly. Which is nothing to sneeze at.

Campbell, W., Mizrahi, J., Quraishi, Q., Senko, C., Hayes, D., Hucul, D., Matsukevich, D., Maunz, P., & Monroe, C. (2010). Ultrafast Gates for Single Atomic Qubits Physical Review Letters, 105 (9) DOI: 10.1103/PhysRevLett.105.090502

drorzel Mon, 08/30/2010 - 05:49

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Measuring Gravity: Ain't Nothin' but a G Thing

drorzel — Thu, 26 Aug 2010 10:25:33 +0000

Measuring Gravity: Ain't Nothin' but a G Thing

There's a minor scandal in fundamental physics that doesn't get talked about much, and it has to do with the very first fundamental force discovered, gravity. The scandal is the value of Newton's gravitational constant G, which is the least well known of the fundamental constants, with a value of 6.674 28(67) x 10^-11 m³ kg-1 s^-2. That may seem pretty precise, but the uncertainty (the two digits in parentheses) is scandalously large when compared to something like Planck's constant at 6.626 068 96(33) x 10^-34 J s. (You can look up the official values of your favorite fundamental constants at this handy page from NIST, by the way...)

To make matters worse, recent measurements of G don't necessarily agree with each other. In fact, as reported in Nature, the most recent measurement, available in this arxiv preprint, disagrees with the best previous measurement by a whopping ten standard deviations, which is the sort of result you should never, ever see.

This obviously demands some explanation, so:

What's the deal with this? I mean, how hard can it be to measure gravity? You drop something, it falls, there's gravity. It's easy to detect the effect of the Earth's gravitational pull, but that's just because the Earth has a gigantic mass, making the force pretty substantial. If you want to know the precise strength of gravity, though, which is what G characterizes, you need to look at the force between two smaller masses, and that's really difficult to measure.

Why? I mean, why can't you just use the Earth, and measure a big force? If you want to know the force of gravity to a few parts per million, you would need to know the mass of the Earth to better than a few parts per million, and we don't know that. A good measurement of G requires you to use test masses whose values you know extremely well, and that means working with smaller masses. Which means really tiny forces-- the force between two 1 kg masses separated by 10 cm is 6.6 x 10^-9 N, or about the weight of a single cell.

OK, I admit, that's a bit tricky. So how do they do it? There are four papers cited in the Nature news article. I'll say a little bit about each of them, and how they figure into this story.

The oldest measurement cited by Nature is the torsion balance measurement from 2000 by the Eöt-Wash group at the University of Washington. This is an extremely refined version of the traditional method of measuring G first developed by Henry Cavendish in the late 1700's.

Let's assume I'm too lazy to follow that link, and summarize in this post, mmmkay? OK. Cavendish's method used a "torsion pendulum," which is a barbell-shaped mass hung at the end of a very fine wire, as seen at right. You put two test masses near the ends of the barbell, and they attract the barbell, causing the wire to twist. The amount of twist you get depends on the force, so by measuring the twist of the wire for different test masses and different separations, you can measure the strength of gravity and its dependence on distance.

Sounds straightforward enough. It is, in concept. Of course, given the absurdly tiny size of the forces involved, it's a really fiddly measurement to do. Cavendish himself set the apparatus up inside a sealed room, and then read the twist off from outside, using a telescope. If he was in the room looking at the apparatus, the air currents created by his presence were enough to throw things off.

This remained the standard technique for G measurements for about two centuries, though, because it's damnably difficult to do better. And the Eöt-Wash group's version is really astounding.

So, how did they do better? One of the biggest sources of error in the experiment comes from the twisting of the wire. In an ideal world, the response of the wire would be linear-- that is, if you double the force, you double the twist. In the real world, though, that's not a very good assumption, and that makes the force measurement really tricky if the wire twists at all.

The great refinement introduced by the Eöt-Wash group was to not allow the wire to twist. They mounted their pendulum, shown at left, on a turntable, and made small rotations of the mount as the wire started to twist, to prevent the twist from becoming big. Their force measurement was then determined by how much they had to rotate the turntable to compensate for the gravitational force causing a twist of the wire.

They also mounted the attracting masses on a turntable, and rotated it in the opposite direction around the pendulum, to avoid any systematic problems caused by the test masses or their positioning. Their signal was thus an oscillating correction signal, as each test mass passed by their pendulum, and they recorded data for a really long time: their paper reports on six datasets, each containing three days worth of data acquisition.

The value they got was 6.674 215 6 Â± 0.000092 x 10^-11 m³ kg-1 s^-2, far and away the best measurement done to that point.

So what are the other papers? The second one, in chrononogical order, is a Phys. Rev. D paper from a group in Switzerland, who used a beam balance to make their measurement. They had two identical test masses hung from fine wires, and they alternately weighed each mass while moving enormous "field masses" weighing several metric tons each into different positions, as shown in the figure at right. In the "T" configuration, the upper test mass should appear heavier than the lower test mass, as the large field masses between them pull one down and the other up. In the "A" configuration, the upper test mass should be lighter, as the field masses pull it up while pulling the lower mass down.

This was another experiment with very long data taking, including this wonderfully deadpan description:

The equipment was fully automated. Measurements lasting up to 7 weeks were essentially unattended. The experiment was controlled from our Zurich office via the internet with data transfer occurring once a day.

Their value, 6.674â252(109)(54) x 10^-11 m³ kg-1 s^-2 is in good agreement with the Eöt-Wash group's result.

If it agrees, why even mention it? It's an important piece of the story, because it's a radically different technique, giving the same answer. It's extremely unlikely that these would accidentally come out to be the same, because the systematic effects they have to contend with are so very different.

Yeah, great. Get to the disagreement. OK, OK. The third measurement, in this PRL by a group in China, uses a pendulum again, but a different measurement technique. They used a rectangular quartz block as their pendulum, suspended by the center, with test masses outside the pendulum. They place these test masses in one of two positions: near the ends of the pendulum when it was at rest (shown in the figure), or far away from the ends (where the "counterbalancing rings" are in the figure).

The gravitational attraction of the masses in the near configuration makes the pendulum twist at a slightly different rate than in the far configuration, and that's what they measured. The oscillation period was almost ten minutes, and the difference between the two was around a third of a second, which gives you some idea of how small an effect you get.

Their value was 6.673â49(18) x 10^-11 m³ kg-1 s^-2, which is a significantly larger uncertainty than the other two, but even with that, doesn't agree with them. Which is kind of a problem.

So, how do you deal with that? Well, they obviously had a little trouble getting the paper through peer review-- it says it was first submitted in 2006, but not published until 2009. That probably means they needed to go back and re-check a bunch of their analysis to satisfy the referees that they'd done everything correctly. After that, though, all you can do is put the result out there, and see what other people can make of it.

Which brings us to the final paper? Exactly. This is an arxiv preprint, and thus isn't officially in print yet, but it has been accepted by Physical Review Letters.

They use yet another completely different technique, this one employing free-hanging masses whose position they measure directly using a laser interferometer. They also have two configurations, one with a bunch of source masses between the two hanging masses, the other with the source masses outside the hanging masses. The gravitational attraction of the 120kg source masses should pull the hanging masses either slightly closer together, or slightly farther apart, depending on the configuration, and this change of position is what they measure.

Their value is 6.672 34 Â± 0.000 14 x 10^-11 m³ kg-1 s^-2, which has nice small error bars-- only the Eöt-Wash result is better in that regard-- but is way, way off from the other values. Like, ten times the uncertainty off from the other values. There's no obvious reason why this would be the case, though. If anything, the experiment is simpler in concept than any of the others, so you would expect it to be easier to understand. There aren't any really glaring flaws in the procedure, though (it never would've been accepted otherwise), so this presents a problem.

So, now what? Well, in the short term, this probably means that the CODATA value for G (the official, approved number used by international physics) will need to be revised to increase the uncertainty. This is kind of embarrassing for metrology, but has happened before-- a past disagreement of this type is one of the things that prompted the original Eöt-Wash measurements.

In the medium to long term, you can bet that every group with a bright idea about how to measure G is tooling up to make another run at it. This sort of conflict, like any other problem in physics, will ultimately need to be resolved by new data.

Happily, these experiments cost millions of dollars (or less), not billions, so we can hope for multiple new measurements with different techniques to resolve the discrepancy. It'll take a good long while, though, given how slowly data comes in for these types of experiment, which will give lots of people time to come up with new theories of what's really going on here.

Gundlach, J., & Merkowitz, S. (2000). Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback Physical Review Letters, 85 (14), 2869-2872 DOI: 10.1103/PhysRevLett.85.2869

Schlamminger, S., Holzschuh, E., KÃ¼ndig, W., Nolting, F., Pixley, R., Schurr, J., & Straumann, U. (2006). Measurement of Newton's gravitational constant Physical Review D, 74 (8) DOI: 10.1103/PhysRevD.74.082001

Luo, J., Liu, Q., Tu, L., Shao, C., Liu, L., Yang, S., Li, Q., & Zhang, Y. (2009). Determination of the Newtonian Gravitational Constant G with Time-of-Swing Method Physical Review Letters, 102 (24) DOI: 10.1103/PhysRevLett.102.240801

Harold V. Parks, & James E. Faller (2010). A Simple Pendulum Determination of the Gravitational Constant Physical Review Letters (accepted) arXiv: 1008.3203v2

drorzel Thu, 08/26/2010 - 06:25

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precision measurement

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Physics

Science

Nice writeup, and I'm ashamed to nitpick about grammar/spelling, but I believe you may have misspelled the word "Thang" in the title.

Ha! It's nice to see you physicists have trouble too.

It looks as if different methods give different results (suggesting they all have different biases). How will you lot know which one is correct?

Also, would altitude make a difference?

What usually happens in this sort of situation is that a few measurements using different techniques will turn out to agree with each other reasonably well, and that will come to be accepted as the "real" value. The data from all of these will be re-analyzed, and eventually somebody will find a plausible systematic effect that could've thrown the results off.

If I had to guess, I'd say that the Eot-Wash result is probably closer to the final value than the newer measurements. The period measurement seems to invite exactly the sort of weird twisting-wire effects that the original turntable measurements were designed to avoid, and the hanging-pendulum thing is, as far as I know, a very new technique, and the most likely to have some subtle problem that hasn't been noticed yet because people haven't been banging on it for decades like the torsion pendulum. That's just a guess, though.

Why do EÃ¶t-Wash give "6.6742156" the extra digits "56" if, by their own estimates, the "2" might just as well be "1" or even "3"?

When I was an undergraduate, G was known to only three digits, so this is progress. I wonder about three-day experiments, though. At this stage they should be collecting measurements for several years before reporting.

Re: Nathan Myers

Re: the digits, I think there's a typo in Chad's writeup and I think you also lost a digit in your reading.

I think the numbers are:
6.674215
with an error bar of
0.000092
(times the appropriate units).

It's standard these days to give 2 digits of error bar, and write your number out to the same length, so I don't think there's anything weird here.

Re: "I wonder about three-day experiments, though. At this stage they should be collecting measurements for several years before reporting."

I disagree for two reasons.

First, precision measurement is partially about statistical error (which you can improve by taking data longer) and partially about checking for systematic errors (which don't improve through averaging). To check for systematics, typically one varies conditions and remeasures things to see how the measured value depends on stuff. To do this well, you may need to take data for almost as long under your "altered" conditions as you do when making them under your "good" conditions. And in most experiments, there are dozens of possible systematics to check. So, a good rule of thumb for a precision measurement experiment is that, when estimating what your statistical error, you allow for a day (or maybe a week) of data taking, so that you can do your systematic checks on the timescale of a couple of years. So I'm guessing that it's not that these guys are lazy or got bored; it's that they're responsible.

Secondly, if you look at their error budget in the paper, the statistical error accounts for 6 ppm error, and their total error is 14 ppm, so taking data for a few years would only make a small improvement to their error, reducing it from 14 to 12 ppm (assuming adding things in quadrature).

If the exact and true value of G is discovered, creating a future time where we say "we should have seen that", it will be because it stands out in theory or is singularly distinctive in other context.

In the use of log tables, it was often necessary to extrapolate a value between those which were actually listed, by discerning the pattern of change and making a prediction. In multidimensional mappings of the values of fundamental constants expressed as common logs, recognizable as multidimensional log tables, there is one
single, unique concurrence of numerical pattern alignments which occurs for a single value of G :

http://www.outlawmapofphysics.com/NGC.pdf

Thanks, AC, that was helpful. I didn't lose a digit; .000092 is close to .0001. But I wouldn't have commented on 6.674215. How should we interpret the values "6.674252(109)(54)" and "6.67349(18)" from the other experiments?

I would have thought that rather than use the torsional modulus of a wire (nonlinearity etc. problems included) and then try to compensate for the nonidealities, more modern approaches to the Cavendish method would have used other sources of extremely small and precise torque.

Such as, to name one, opposing lasers from the same direction as the stationary masses.

The question of "measuring G" leads to a related, deeper (and somewhat "philosophical") questions: is G is one of those constants with MLT dimensions, like c, that it's impossible to unambiguously talk about the value of in other than relative terms? Hence, you can't just say e.g. "if c was ten times greater, then ...." (although George Gamow did what he could in the clever, mass-accessible "Mr. Tompkins in Wonderland.") If we imagine c different, then other things have to change along with it and it's hard to see how we could define or tell the difference. (More complicated than "what if everything got bigger," but still a definition issue.) We can presumably triangulate some relations in simple atomic physics while forgetting the nuclear part, such as being able to know if the relationship between electron mass, e, h, c, etc, have changed.

Yet even though G has units (L^3/MT^2), I think it is rather intuitively clear what it means to say "what if everything was the same, except G was different." We can IMHO rather easily imagine what physics would be like (most experiments anyone does: no difference, including G = 0 or even negative, as long as G was not imagine much bigger than now) and indeed imagine ways to test G separately. Some folks even thought G might change over long time scales. They must not have imagined an intrinsic contradiction: they conceived and and looked for evidence. (None was found AFAIK.)

It is true we have to imagine mass "staying the same" while G changes, but there are other measures of mass if we accept some triangulation from other features. We can just say, the familiar particles "being the same mass in every other way" as well as constant charge, h, etc. which implies no alteration in atomic physics. Yet I suppose it could be fun to imagine how much you'd need to fiddle to hide an attempted change of G in other ways.

I suspect that G may in fact be only approximately constant and that it's value does depend weakly on the local composition of matter.

Are there any good reasons to exclude such a possibility?

And yes, I know it demotes GR to an effective theory.

I wonder if you can really do this in the basement:
http://www.fourmilab.ch/gravitation/foobar/

The arXiv abstract for the latest measurement states that the value is in good agreement with the accepted 1986 CODATA value but not, as stated, the latest value.

I guess it's interesting how an 'accepted' value changes with time and highlights how difficult it is to make good uncertainty estimates - the CODATA uncertainties don't overlap so somebody was being optimistic.

The EÃ¶t-Wash quadrupole balance is error-correcting marvelous in so many ways. Dipole measurements are historically divergent. However, the EÃ¶t-Wash balance has only used a fused silica plate, a low atomic number glass. It would be interesting to repeat the measurement with

1) a single crystal silicon plate of surpassing purity, SOP in the semiconductor industry. Big G pendula might detect magnetic impurity atoms even in low numbers.

2) a high atomic number plate. Pt-Ga,In alloys heat treat to tool steel hardness and stiffness for shaping; Niessing Co., Hoover and Strong Pt SK alloys, Eastern Smelting HTA Pt alloys. Alloys are ~95 wt-% platinum.

3) A space group P3(1)21 single crystal quartz plate. Sawyer Technical Materials LLC grows X-plate quartz to astounding perfection. (Commercial Grade C Z-plate quartz is space group P3(2)21. That is not geometrically interesting, nor is it especially compositionally pure or free of dislocations.)

Given how sensitive these experiments are, there are too many factors at play to have a truly controlled environment.

For example, how would one detect and factor in an anomalous amount of mass (or lack thereof) in one direction? An large and unknown underground cavern 1/2 kilometer underground/away can throw off the experiment if the experiment just happens to be positioned the wrong way.

Perhaps the best way to get uniform data is to perform some of these brilliant experiments in (or immediately outside) of an orbital station.

The arXiv abstract for the latest measurement states that the value is in good agreement with the accepted 1986 CODATA value but not, as stated, the latest value.

The 1986 value had really gigantic error bars, so that's not terribly surprising. The Eot-Wash value also agrees with the 1986 CODATA value, in a fairly narrow sense.

They know a lot about the local mass distribution. I saw a talk by somebody from the Eot-Wash group that included a picture of their lab. In the middle of the floor a few meters away from the apparatus was a big stack of lead bricks, which he explained were placed there to compensate for the fact that the building they're in is on the side of a large hill.

It's a known problem, and something they incorporate into their error analysis.

Nice article, I don't know much about physics and gravity but had a idea from your post. I have learned few things and will continue reading the site. Bookmarked and will visit daily.

This is just crazy, they should go with approximate gravitation value ;-)

Seriously, The fact that there are some differences in measurements means that additional factors are missing from the equation.

I agree with Neil B above. I could never understand how "mass is constant". There have to be x number of assumptions to get that right. That's common sense. I don't see those assumptions being clearly laid out in books and reports!

[Given how sensitive these experiments are, there are too many factors at play to have a truly controlled environment.

Perhaps the best way to get uniform data is to perform some of these brilliant experiments in (or immediately outside) of an orbital station.]
totally agree with you

@Neil @ Nick (18):
Or do all methods in the same lab at the same time. Then they'd all be under the same conditions

Laws of Physics, or Merely Local By-laws?
Written By: Jonathan Vos Post
Date Published: September 9, 2010
http://www.hplusmagazine.com/editors-blog/laws-physics-or-merely-local-…

@ Anonymous Coward:
The "mispelling" of the word "Thang" is actually a play on words about gravity and Dr. Dre/Snoop Dogg's rap song "Ain't Nuthin but a G Thang". Here the joke is that really the calculating a precise value for the gravitation constant G - is Nuthin But a G Thang.

At some point the results will have to be repeatable with a standardised machine. Hallmark! No there is no progress yet within Codata of going from one value (gravitational constant only) to the next as this is extremely difficult. After Luther-Towler's result Codata 1986 there was a collapse to 3-4 digits (Codata 1998) due to different results creating a large uncertainty fluctuation. It looks like this may happen again but it will not be as bad. So a new gravitational constant number in Codata is not necessarily a sign of a step forward just yet. Actually I like this trending down back to Luther-Towler as their results may actually be repeatable and machine was simple. Also, just because two different apparatuses get a similar number is not cause to celebrate as this has happened time and again with the history of this number. The other values in Codata such as masses and the fine structure constant etc. are actually progressing along.

Well, we have a couple of other problems to contend with, such as the fact that there are measurable "tide" effects from the Earth, Moon, Sun three body system, which are time varying. Their magnitude is on the order of multiple microGals to tens of microGals. This time varying signal needs to be incorporated in terms of frequency and amplitude to ensure that the long period measurements are actually statistically canceling out these effects, and not biasing the results.

I'm surprised not to see any accounting for the large tidal effects of Jupiter and Mars along with the usual Sun and Moon. As we all know, each time the outer planets are in conjunction all manner of catastrophes occur here on Earth (earthquakes, tsumamis, buildings topplingâ¦). A little basic astrology could easily account for the error in these measurements.

Melting Simulated Insulators

drorzel — Wed, 25 Aug 2010 07:23:59 +0000

Melting Simulated Insulators

The Joerg Heber post that provided one of the two papers for yesterday's Hanbury Brown Twiss-travaganza also included a write-up of a new paper in Nature on Mott insulators, which was also written up in Physics World.

Most of the experimental details are quite similar to a paper by Markus Greiner's group I wrote up in June: They make a Bose-Einstein Condensate, load it into an optical lattice, and use a fancy lens system to detect individual atoms at sites of the lattice. This lattice can be prepared in a "Mott insulator" state, where each site is occupied by a definite number of atoms. As the total number of atoms in the BEC increases, the number per site increases, and forms a set of "shells" with, say, exactly two atoms per site in the center, surrounded by a shell of one or two atoms per site, surrounded by a shell of exactly one atom per site, and so on.

The thing that sets this paper apart is a temperature-dependent effect, which appears as Figure 5, which I reproduce here:

So, what's this figure, besides really complicated and orange-y? It is pretty orange, isn't it? SteelyKid came downstairs while I was reading it, looked at the image on screen, and said "Fire, hot! Careful!"

This picture shows the "melting" of the Mott insulator as the temperature is increased. The three images at the top are pictures of the trapped atoms at different temperatures, increasing from left to right. You can see that the shells get less regular as the temperature increases-- there's still a clear shell structure in part c, but it's not as distinct as part a.

Wait, I thought this was a BEC? Isn't that as close to absolute zero as you can get? Yes and no. The way the cooling method works, you selectively remove the most energetic atoms from the trap, using the fact that they tend to be found around the outside edge of the atom cloud. This "evaporative cooling" is essentially the same as what happend to a cup of coffee or tea left sitting on your desk-- the hot atoms evaporate away, and what's left behind is colder.

Eventually, you reach a point where the atoms condense into a BEC, with most of the atoms occupying a single quantum state, the lowest-energy state of the trap. This doesn't mean it's at absolute zero, though, because even in the best experiments you still have a small fraction of the atoms existing in energy states above the lowest energy. And you still have fluctuations in the number of atoms in the BEC-- they can occasionally pop out into higher energy states, then fall back into the condensate.

This means that even after the formation of the BEC, there's still a temperature associated with the sample. You can continue evaporative cooling after the formation of the BEC, and you will continue to lower the temperature of the sample.

(They're a little vague about how the temperature variation is obtained, but I think they're varying the amount of evaporative cooling below the BEC point. At least, I can't really think of another way they would be doing it in a controlled manner.)

So, this temperature acts to melt the insulator? Right. Because the atoms have a temperature, there's a little bit of random extra energy floating around, that can be used to move atoms from one site to another. As you increase the temperature, more and more atoms will hop out of where they're supposed to be, making your "shells" less distinct.

And the graphs at the bottom show this in some way? Right. The key thing to compare to is the grey points and line, which are data from a "zero temperature" cloud (evaporated far enough that there's very little effect of fluctuations) that's not one of the pictures in the figure. The upper graph shows the average number of atoms per site, and the lower graph the variance in the atoms per site, plotted as a function of the "local chemical potential" which is a measure of the distance from the center of the cloud and the number of atoms at that distance (to account for the fact that the density of atoms drops off as you go out).

The grey line shows exactly the behavior you expect for a Mott insulator. There's a flat bit at the start where the average occupation is zero, then a region where it shoots up to one atom per site, then it drops back down. The variance in the number of atoms per site is zero at the beginning, and zero in the region where the average number is flat, and shows two peaks in the region where the average number is changing rapidly.

Then the orangey lines are the pictures at the top? Right. The nearly invisible yellow is the lowest temperature (part a), the orange is the middle (part b) and the red is the highest temperature (part c). You can see that the signal gets less distinct as the temperature increases. The peak occupation number goes down, while the variance goes up. The lines are fits to the data, used to extract the temperature and other parameters.

That doesn't look like much variation. Couldn't they have gotten some data in the big empty space between the grey and yellow lines? In principle, probably. In practice, this is a damnably difficult thing to control, as the number of atoms changes really dramatically when you try to increase the temperature. These are almost certainly the best images they were able to get that have the right number of atoms at non-"zero" temperatures.

So, how does this help us make flying cars, again? It's not something that's going to immediately give you a technological breakthrough-- we're talking thousands of atoms here, not anything close to a macroscopic object. This sort of imaging does give you a really nice probe of the behavior of the atoms in a system where they mimic the behavior of electrons in a superconductor, though, and lets you look at details that are really difficult to observe in a more traditional condensed matter system. The direct measurements of variance and thermal effects also give you a neat way to play with the thermodynamics and statistical physics of the system, looking at things like the movement of entropy through different parts of the system.

It's not going to get you a flying car or a perpetual motion machine, but it's a cool tool for looking at condensed matter type problems in a way that you couldn't do before. And new experimental tools are always a good thing.

Sherson, J., Weitenberg, C., Endres, M., Cheneau, M., Bloch, I., & Kuhr, S. (2010). Single-atom-resolved fluorescence imaging of an atomic Mott insulator Nature DOI: 10.1038/nature09378

drorzel Wed, 08/25/2010 - 03:23

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SteelyKid came downstairs while I was reading it, looked at the image on screen, and said "Fire, hot! Careful!"

Sounds like you're not the only scientist living at Chateau Steelypips. I'll grant that she doesn't fully understand this result, but she seems to have noticed a correlation between fire/heat and certain things melting, as is happening here.

Why do the gray data points not continue as far to the right as the orange/red ones?

Thanks Chad for linking my blog post!

With respect to the unclear description of how they vary the temperature, it also took me some digging in their older papers, but as I eventually understood it, this is not done by changing the temperature of the atoms, but by changing the potential of the optical confinement field, i.e. reducing laser intensities. So you don't "lift" the energy of the atoms but reduce the confinement potential. Gives you a much better accuracy.

Until I read this blog offline, I have no idea what it means, but "Melting Simulated Insulators" has to be one of the best blog titles ever. It sounds like the title of an anime or a manga!

Bunches and Antibunches of Atoms: Hanbury Brown and Twiss Effects in Ultracold Atoms

drorzel — Tue, 24 Aug 2010 08:13:39 +0000

Bunches and Antibunches of Atoms: Hanbury Brown and Twiss Effects in Ultracold Atoms

Two papers in one post this time out. One of these was brought to my attention by Joerg Heber, the other I was reminded of when checking some information for last week's mathematical post on photons. They fit extremely well together though, and both relate to the photon correlation stuff I was talking about last week.

OK, what's the deal with these? These are two papers, one recent Optics Express paper from a week or so ago, the other a Nature article from a few years back. The Nature paper includes the graph you see at right, which is a really nice dataset demonstrating the Hanbury Brown and Twiss bunching effect in bosonic helium-4 (top), and the analogous anti-bunching effect in fermionic helium-3 (bottom).

Very pretty. Who are Hanbury, Brown, and Twiss, and why should I care? There are only two of them-- Hanbury Brown has a double unhyphenated last name, so its really the (Hanbury Brown) and Twiss effect. Hanbury Brown and Twiss were a couple of British astronomers working on a way to make an interferometer to measure the size of nearby stars. They were looking at intensity correlations between the signals from two telescopes looking at the same star, and using that information to measure its angular size.

As a sort of demonstration, they looked at the signal from a bench-top light source, and showed that the light signal showed bunching-- that is, they were more likely to detect a second bit of light very shortly after the first bit than they were to get more light at longer times. While this is easily explained and in fact inevitable in a wave model of light (as I explained last week), it created a bit of a stir among people in the then-new field of quantum optics (Hanbury Brown and Twiss did their experiment in the 1950's), as this didn't seem like something you should get from a photon model of light. It took a little while to sort out, but the ultimate explanation is really very simple.

And that is? Photons are bosons.

Photons, like protons and electrons and nearly all other fundamental particles, have intrinsic angular moment called "spin." Unlike electron spin, though, photons have one unit of angular momentum, not just half a unit. This has dramatic consequences for the symmetry of the wavefunctions used to describe the system-- where fermionic particles like electrons are forbidden to be in the same place at the same time, bosonic particles like photons will happily cluster together in a single quantum state.

One of the consequences of this is that bosons will tend to bunch up in a beam, so that the probability of detecting a second one right after the first is higher than the probability of the second one coming much later. That's exactly what Hanbury Brown and Twiss saw, and what everybody else to look at correlation functions for photons has seen.

So, if they figured this out in the 50's, why are people writing about it now? People figured this out for photons back in the 1960's, but it hasn't been possible to do it with atoms until more recently.

Wait, atoms and photons aren't remotely similar. Atoms are made up of protons and neutrons and electrons, which are all fermions. True, but if you stick an even number of fermions together, each with half a unit of angular momentum, you can make a composite boson, with an integer number of units of angular momentum. That composite object will show the Hanbury Brown and Twiss effect, as long as the energies involved are small. If you take an odd number of protons, neutrons, and electrons and stick them together, the resulting atom is a composite fermion, and will show the effects of Pauli exclusion-- that is, you will never see two atoms in the same state at the same time, leading to anti-bunching.

So that's what these papers are about? Doing the same thing with atoms that people did with light a long time ago? Yep. The Nature paper is looking at the correlation behavior of two different isotopes of helium, the bosonic isotope helium-4 and the fermionic isotope helium-3. They took laser-cooled clouds of one isotope or the other, and dropped them onto a position-sensitive detector, then looked at how many pairs of atoms arrived together.

How did they do that? Helium, like all the other noble gases, can't be cooled in its ground state with current laser technology, but has a metastable state that lives essentially forever, and can be used as the ground state for a laser cooling experiment. Each one of these metastable atoms carries a huge amount of energy-- more than 10 eV-- which is enough to knock an electron loose from anything they hit. If you drop metastable helium atoms on a microchannel plate detector, many of the He atoms will knock electrons loose. These electrons can then be amplified into a measurable current pulse, and the pulses can be counted electronically.

You can also direct some of the electrons from the MCP onto a phosphor screen, where they'll show up as little flashes of light. This gives you the full spatial distribution of the atoms as they hit the plate-- the horizontal dimensions from the position of the spots on the phosphor, and the vertical from the distribution of arrival times.

This lets them measure correlations? Yes. They look at how often they saw two atoms arriving within some distance of one another, and used that measurement to determine the correlation function shown in the graphs above. When they did the experiment with helium-4, they found an increased probability of detecting two atoms in rapid succession, and when they did it with helium-3, they saw a decreased probability of detecting two atoms in rapid succession, just as you would expect.

(This was not, by the way, the first such measurement-- a Japanese group demonstrated the Hanbury Brown and Twiss effect in 1996 with metastable neon. The Nature paper is the first to show the anti-bunching effect, though, and has a cleaner signal with the bosons, thanks to (among other things) the fact that they used a much colder sample.)

The correlation function only changes by, what, 5%, though. That's not that big. Yeah, but this is a really difficult experiment to do-- everything has to work just right, and you need to do a whole lot of data taking to pick out the signal. In an ideal world, the bunched signal would go all the way up to 2, and the anti-bunched signal would go down to 0, but we don't live in an ideal world, so any clear effect at all is pretty darn cool.

OK, so, if people did these experiments in 1996 and 2007, why are they still writing it up in 2010? The second paper, from Optics Express looks at a different twist on the same experiment. They work with just the bosonic isotope, and compare what happens with a normal cloud of very cold atoms (top graph in the figure below) to what happens when they start with a BEC (bottom graph):

The BEC graph is just a flat line. Bor-ing. Actually, that's the exciting result. You can see the same thing with photons, if you compare light from a lamp to light from a laser. The laser gives the same sort of flat correlation function, because the laser is a source of coherent light, which means that the intensity fluctuations are as small as they can possibly be. A laser behaves like a classical light wave to a very good approximation, and one signature of that behavior is a flat correlation function.

(In the photon picture, a laser is represented by a "coherent state" which has the nifty property that subtracting one photon from it doesn't change the state. Such a coherent state is the best approximation of a classical EM wave that you can make.)

So, a BEC is a laser? It's analogous to a laser, for atoms. It's not an analogy that can be pushed too far-- the real reason lasers are technologically useful is that they are really, really bright. The typical "atom laser" has only millions of atoms, which is about a nanosecond's worth of light from a typical laser pointer, so the technological potential isn't anywhere near as great.

BEC's do share the coherence properties of laser, though, including the flat correlation function. And that's what this new experiment shows: they looked at atoms dropped from a cloud just above the BEC transition temperature and saw the usual Hanbury Brown and Twiss bunching, then compared that to atoms dropped from a cloud just below the BEC transition, and saw a flat correlation function.

It's a cute demo, I guess, but is it good for anything? Well, it tells you that atoms coupled out of their BEC share the coherence properties of the whole thing, which is worth knowing. The technique could potentially be used to test the behavior of various "atom laser" schemes.

It's not as sexy as the other paper, though. Which explains why it's in Optics Express rather than Nature.

So, anyway, that's what's up with correlating atoms. Any more questions?

Jeltes, T., McNamara, J., Hogervorst, W., Vassen, W., Krachmalnicoff, V., Schellekens, M., Perrin, A., Chang, H., Boiron, D., Aspect, A., & Westbrook, C. (2007). Comparison of the Hanbury Brown-Twiss effect for bosons and fermions Nature, 445 (7126), 402-405 DOI: 10.1038/nature05513

Manning, A., Hodgman, S., Dall, R., Johnsson, M., & Truscott, A. (2010). The Hanbury Brown-Twiss effect in a pulsed atom laser Optics Express, 18 (18) DOI: 10.1364/OE.18.018712

drorzel Tue, 08/24/2010 - 04:13

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I'm a bit confused about the x-axes of these plots: On the first plot, we have correlation versus separation (between what?), but the later plots show correlation versus time.

Even if we disregard this discrepancy, I'm not sure why the non-BEC atoms become correlated only after a certain amount of time (or separation). Are the atoms condensing into a BEC over the course of the measurements?

I'm a bit confused about the x-axes of these plots: On the first plot, we have correlation versus separation (between what?), but the later plots show correlation versus time.

They're both ways of measuring the separation between atoms. The time measurement is the amount of time that passes between the first and second atom detected in some region of the detector, the distance measurement is the distance between the first and second atoms when they strike the detector. For the graph shown, they're looking at the vertical distance, so this is really the speed at which the atoms strike the detector (which is a known quantity, as they're dropped from rest a known distance above the detector) multiplied by the difference in arrival times.

The atoms that are in a BEC start out in a BEC before they're dropped. The correlation between non-BEC atoms actually disappears after some time-- the higher the plotted quantity, the higher the probability of finding a second atom at that distance (in space or time) from the first atoms detected.

Very interesting article. I have one question concerning this part: "In an ideal world, the bunched signal would go all the way up to 2, and the anti-bunched signal would go down to 0, but we don't live in an ideal world, so any clear effect at all is pretty darn cool."

Do composite objects really have clear fermionic or bosonic character? I would think it's just an approximation in this case.

For example helium 4 may mostly behave like a boson but it's still composed of fermions which cannot be in the exact same location and quantum state so two helium 4 atoms cannot occupy the exact same location and quantum state either.

So this would mean that as the distance approaches zero the correlation between composite bosons should eventually start going down to zero. Of course this would only happen once the separation is comparable to atomic scale and not for millimeters as in the plot.

Do composite objects really have clear fermionic or bosonic character? I would think it's just an approximation in this case.

It's an approximation, but a very good one. In order for one helium atom to "see" that the neighboring atoms were really composite particles, you would want them to be separated by something close to the size of the atoms themselves, which is something like a tenth of a nanometer. The atoms in these experiments are at densities of a few times 10^18 per cubic meter, which corresponds to a separation of hundreds of nm. They're nowhere near tightly packed enough for this to be a problem.

High Excitement in Review: "Quantum information with Rydberg atoms"

drorzel — Mon, 23 Aug 2010 09:34:22 +0000

High Excitement in Review: "Quantum information with Rydberg atoms"

I'm a big fan of review articles. For those not in academic science, "review article" means a long (tens of pages) paper collecting together the important results of some field of science, and presenting an overview of the whole thing. These vary somewhat in just how specific they are-- some deal with both experiment and theory, others just theoretical approaches-- and some are more readable than others, but typically, they're written in a way that somebody from outside the field can understand.

These are a great boon to lazy authors, or authors facing tight page limits ("Ref. [1] and references therein" takes up a lot less space than individual citations for the ten most important historical papers), and also to people who would like to get a technical introduction to a new field. They have a slight tendency to overemphasize the particular interests or results of the people writing the review, but that's not too big a distortion, provided the authors are chosen well.

The journal Reviews of Modern Physics is primarily review articles of this type, and a recent paper there caught my eye as something worth talking about on the blog. Hence this post.

Waitaminute-- do you seriously expect us to wade through 51 pages of a physics article? No, not really. Not unless you really want a thorough overview of the field. It's more that this is an area of work that is generating some interest these days, and this article is a convenient collection of the important results. You don't need to read the whole thing, though-- you can just skim it for the good parts if you like.

All right, then. So, what do loathsome bipedal crustaceans have to do with quantum information? That's a Zoidberg, not a Rydberg. A "Rydberg atom" is an atom in a highly excited state, very close to the ionization limit-- technically, it probably ought to be "quantum information with atoms in Rydberg states," but "Rydberg atom" is well established jargon and there's nothing to be done about it now.

The name comes from the Rydberg formula, which was the first really good description of the emission spectrum of hydrogen, which Niels Bohr eventually showed could be interpreted as describing transitions between discrete electronic states of the atom. The Rydberg formula only works well for the low-lying states of hydrogen, because interactions between the electrons in more complicated atoms (i.e., everything else) shift all the energy states. If you take one electron and excite it to a very high level, though, the states up there start to follow something like the Rydberg formula again.

What do you mean, "very high level?" Well, the transitions in hydrogen that produce visible light are between levels with a quantum number of 3, 4, 5, or 6 and a level with a quantum number of 2. Rydberg states in other atoms have quantum numbers of 30 or more, sometimes as high as a couple hundred.

OK, that's pretty high. What do these have to do with quantum information? Well, the idea of using Rydberg states in quantum information is to try to find a way around the somewhat contradictory requirements for a quantum computer. If you want to do quantum information processing with a reasonable number of "qubits," you need a system that on the one hand is well insulated from the environment, so your bits don't flip randomly, but on the other hand, you need to be able to couple the bits together strongly so that you can entangle the states of different bits. Finding systems that will give you the right balance between these two requirements is a big part of research in quantum computing.

Ground-state neutral atoms in optical lattices are one possible system, and they offer good insulation from the environment-- it takes a substantial amount of energy to excite an atom from the ground state, and by definition, they don't have anywhere to decay to, so they can have very long lifetimes. Their interactions are extremely weak, though, so it's tricky to do entangling operations between them. You can set up situations where you can entangle the states of neighboring atoms, but this tends to be slow, and the atoms involved are generally very close together, which makes it difficult to address them individually, which is another key element of a quantum computer.

So how can exciting them to very high states help? Doesn't that just give them lots of places to decay to? Yes and no. You do get a lot of possible decay paths, but it turns out that the lifetime of a Rydberg atom increases as you increase the quantum number-- it scales like the quantum number n cubed, so if you go to high Rydberg states, the atoms will stay there a good while. More importantly, the interactions between them scale like n to the fourth power, so two atoms in Rydberg states will interact strongly while they're separated by distances so large that neutral atoms wouldn't notice each other at all.

Yeah, but doesn't that just make them fall apart really quickly? It could, but the key to most of these schemes is to keep the atoms in the Rydberg state for only a short time. Basically, you use two ground states as the "0" and "1" states for your qubit, and use excitation to the Rydberg state as a means of entangling two nearby atoms.

How does that work? There are two main ways to do it. The simplest uses "Rydberg blockade," which stops atoms from being excited if there's another atom already in the Rydberg state. The interaction can be strong enough that if you have one atom already excited to the Rydberg state, and try to excite another one, the interaction between the already-existing Rydberg and the one you're trying to create is so strong that it changes the laser frequency you would need to use, and blocks the excitation.

You can use this to do an entangling operation between a "control" qubit and a "target" qubit. First, you hit the atom serving as your control qubit with a laser that excites the "1" state to a Rydberg level, but leaves the "0" state alone. Then you hit the target atom with a laser pulse that should excite the "1" state to the Rydberg level, then drive it back to the "1" state.

If your control qubit is in the "0" state, nothing interesting happens. If the control qubit starts out in the "1" state, though, this stops the target from being excited, which gives the resulting wavefunction a different phase than it would've had otherwise. That control-dependent phase shift allows you to construct a quantum gate that entangles the states of the control and target qubits, and it turns out you can use these gates to do all of the operations you would need to do for a quantum computer.

So you entangle the two by not exciting one. That's kinda cool. Yeah. The other method is to actually excite both, and let the interaction between them in the Rydberg state provide the entangling phase shift. This doesn't need as strong an interaction as the blockade mechanism, but it involves more time spent in the Rydberg state, which slightly increases the chance of errors.

So, this actually works? They're in a very early stage, but the basic idea is sound. The review article includes a nice summary of the current state of the experiments, including demonstrations of the state changes that you need to make for the quantum computing operations, and also some demonstrations of the blockade effect. The operation fidelities are nowhere near what they'd need to be for a real quantum computer-- some of their key steps work about 80% of the time, rather than the 99%+ you would need to build a useful computer-- but it's an early stage, and these are cool experiments in their own right.

So, be honest now, is this going to be the killer technology needed to make a quantum computer? I wouldn't put money on this, no. But it's good, solid physics, and the process of doing these experiments will teach us a lot about the manipulation of atomic states and quantum information, and that's always a good thing. There may even be particular problems for which this is the right quantum simulation approach-- we'll have to wait and see.

If you want to know what the current state of the subfield is, though, this review is a good place to look.

Saffman, M., Walker, T., & MÃ¸lmer, K. (2010). Quantum information with Rydberg atoms Reviews of Modern Physics, 82 (3), 2313-2363 DOI: 10.1103/RevModPhys.82.2313

drorzel Mon, 08/23/2010 - 05:34

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