precision measurement

The Test(ing) of Time 2: Freezing Time

drorzel — Tue, 12 Jul 2011 08:32:45 +0000

The Test(ing) of Time 2: Freezing Time

A month and a half ago, I reported on a simple experiment to measure the performance of a timer from the teaching labs. I started the timer running at a particualr time, and over the next couple of weeks checked in regularly with the Official US Time display at the NIST website, recording the delay between the timer reading and the NIST clock.

As a follow-up experiment, I did the same thing with a different timer, this one a Good Cook brand digital timer picked up for $10 in the local supermarket, and the same Fisher Scientific stopwatch/timer as the first experiment, with the Fisher Scientific timer thrown into the mini-fridge in the lab across the hall between measurements. The results look like this:

The red points are the data from the original test of the stopwatch, the blue points are the timer in the fridge, and the green points are the supermarket timer. The vertical axis is the delay between the two (all three ran slow compared to the NIST clock), and the horizontal axis is the elapsed time between starting the timer and a given measurement.

As you can see, this more or less agrees with what you would expect. The timer that is sold as a piece of laboratory equipment is the best of the lot, with the cheap kitchen timer being slightly less accurate. Putting the stopwatch in an environment that is significantly colder than room temperature (the average temperature recorded by an indoor-outdoor thermometer with its outdoor probe sitting in the mini-fridge was something like -3C) significantly degrades its performance, as you would expect for a timer based on a physical artifact (presumably a quartz crystal).

All three data sets are beautifully linear, with slopes of (1.016+/-0.00033)x10^-5 (for the stopwatch), (3.336 +/- 0.0013)x10^-5 (for the cold stopwatch), and (1.538 +/- 0.0017)x10^-5 (for the Good Cook timer). The uncertainty for the more recent runs is a little larger, possibly because I was a little more casual about recording these, but also because I didn't take data for as long in the second experiment.

The dramatic difference between the cold stopwatch and the same watch at room temperature gives you a good idea of what clockmakers have to contend with when making precision timepieces. If you were relying on one of these as a navigational instrument, it would do vastly better in the summer than in the winter (or in warmer climates than colder ones), which could be a major issue for someone running a shipping business. That's why the John Harrison is justly celebrated, and why the Longitude Prize he was chasing was such a big deal.

The next obvious extension of this would be to borrow a couple more stopwatches from the teaching labs and test Fisher's quality control. I think I've accomplished more or less what I hoped to at this point, though, so I'll move on to other things.

drorzel Tue, 07/12/2011 - 04:32

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Most portable timers/stop-watches/etc. are based on the piezoelectric properties of Quartz crystals as the time reference. The resonant frequency of a piece of Quartz is related to it's dimensions/mass, as well as vibration mode being exploited, as well as the "cut" of the slab. Temperature affects this, but in unexpected ways. Depending upon the "cut" of the slab of Quartz from the raw crystal (e.g., displacement of the slab being cut from the X-Y-Z axes), it's possible to have an "S" shaped temperature coefficient. Ideally, by tweaking the cut, one can obtain a near zero temperature coefficient over a small range near room temperature (or, over a small range at an elevated temperature, which makes putting the crystal in a temperature controlled oven much easier).

Your mission, if you choose to accept it, is to find out how the error in the timers/stop-watches varies given a range of temperatures different from room temperature.

Dave

So you've just demonstrated what everyone knows, which is that time runs slower the closer you get to 0 deg K?

So it's not relativistic time dilation.

Babaganoosh here and this was such a treat, boost out another one asap

What's So Interesting About AMO Physics?

drorzel — Tue, 28 Jun 2011 10:15:48 +0000

What's So Interesting About AMO Physics?

That's the title of my slightly insane talk at the DAMOP (Division of Atomic, Molecular, and Optical Physics of the American Physical Society) conference a couple of weeks ago, summarizing current topics of interest in Atomic, Molecular, and Optical Physics. I'll re-embed the slides at the end of this post, for anyone who missed my earlier discussion.

I put a ton of work into that talk, and had a huge amount of material that I didn't have time to include. I'd hate for that to go to waste, so I'm going to repurpose it for blog content over the next week or so. It'll probably be about a half-dozen posts all told, which should give you some idea of how crazy it was to try to pack all this material into a single talk.

As I note in the slides, the reason for the summary talk in the first place was that the DAMOP meeting has gotten much larger over the last ten or fifteen years. I happened to have a copy of the 2001 program among the junk in my office, and this year's meeting was almost twice as big as ten years ago: the number of talks increased from 270 to 477, and the number of posters from 293 to 548. It's still a long way from the March Meeting, but it's getting difficult to keep track of all the different things going on.

To impose a little structure on the vast amount of material I was trying to summarize, I identified five broad areas of current research interest, and highlighted one invited-talk session from each area. The selection of areas and topics to highlight was a little idiosyncratic-- this was definitely my opinion of what's most interesting in AMO physics, and a different speaker might've broken things down differently. The categories I used are:

--Ultracold Matter: This was the largest single category in terms of the number of invited-talk sessions, and is probably the largest overall, including all the contributed sessions as well. It's also my "home" in the field, as my professional background is in laser-cooled atomic collisions and BEC. Thus, it gets to go first.

The study of ultracold atomic systems typically begins with laser cooling, using light-scattering forces to slow the motion of atoms, and accumulate large numbers of atoms in a vapor at microkelvin temperatures (that is, 0.000001 K, or one one-millionth of a degree above absolute zero). The 1997 Nobel Prize in Physics went to Chu, Cohen-Tannoudji, and Phillips (my Ph.D. advisor) for the development of laser cooling back in the mid-1980's.

While there are still interesting things being done just with laser-cooled samples, microkelvin temperatures really only count as "cold" these days. "Ultra-cold" generally requires a further step, evaporative cooling, where the highest-energy atoms are selectively removed from the sample, lowering the average energy of the remaining atoms. After some collisions to redistribute the energy, you're left with a sample that is colder, and also typically denser. Through a process of repeatedly removing "hot" atoms and letting the rest rethermalize, a laser-cooled vapor at microkelvin temperatures densities a billion times lower than room-temperature air can be cooled and compressed until it forms a Bose-Einstein Condensate (which I explained to Emmy in this Seed article), with typical temperatures in the nanokelvin range, and densities a million times lower than air. the 2001 Nobel Prize in Physics went to Cornell, Ketterle, and Wieman for making the first BEC's in dilute atomic vapors.

There are a whole slew of things people do with BEC, studying fundamental atomic properties, making precision measurements, looking at condensed matter physics and thermodynamics. It's an incredibly versatile tool for basic research, and that's why it's one of the largest areas of current research in DAMOP.

--Extreme Lasers: In the last twenty-odd years, there has been a huge amount of work on pushing the limits of laser technology. As a result, it is now relatively easy to make lasers that produce pulses only a few femtoseconds in duration (1fs = 0.000000000000001 s). These pulses also tend to pack a great deal of energy into the short pulse, so the electric field associated with the laser pulse can be strong enough to highly ionize any material it encounters, which opens a huge range of possibilities. One of the student speakers in the undergraduate session was even looking at situations where the field strength becomes great enough to produce electron-positron pairs from the vacuum (theoretically, not experimentally. Not yet.)

The availability of ultra-fast and ultra-intense pulses opens a lot of possibilities for exciting physics. Short pulses allow you to follow atomic and molecular dynamics on the time scale of the motion of the electrons, which is pretty amazing. High intensities allow the creation of strongly ionized systems, which have interesting properties of their own, and can allow things like laser wakefield acceleration. The dynamics of the electric field interacting with a sample of gas can lead to processes where extreme ultraviolet and even x-ray beams are produced in a coherent fashion, using "table-top" sources. And femtosecond lasers even find applications in precision metrology, through "frequency comb" sources (which won a share of the 2005 Nobel Prize in Physics).

--Quantum Phenomena: Single atoms and molecules are inherently quantum systems, and thus provide a very nice test bed for lots of quantum phenomena. In recent years, it's also become relatively easy to make "non-classical" states of light, that have to be described in terms of discrete numbers of photons, and these, too are rich sources for studying quantum phenomena.

Roughly speaking, there are two major areas of interest in this subject: quantum information processing, and quantum communications. Quantum information processing, as the name suggests, is about building quantum computers, replacing classical "bits" with "qubits" that can be in a superposition of "0" and "1" at the same time. The internal states of atoms and molecules can readily serve as the logical states for information processing, and the interatomic interactions that AMO physicists have been studying for decades provide a variety of clever ways to couple these qubits together to do computations.

Quantum communication is about moving quantum information from one place to another, or between different forms. This involves things like quantum cryptography, where pairs of photons are used to generate "unbreakable" codes; quantum teleportation, where arbitrary states are moved from one place to another without measuring them in the process; and the exchange of quantum information between light and matter, for example, by taking the state of an atomic qubit and converting it to a superposition of polarization states of a single photon.

This is a large and very active field at the moment. Nobody has won any Nobel Prizes for quantum information science, but it's probably only a matter of time. (Aspect, Clauser, and Zeilinger would be a great set of laureates, or Aspect, Wineland, and Zeilinger).

--"Traditional" AMO Physics: This is a slightly vague "what I'm pointing at when I say 'traditional'" sort of category, which basically boils down to the study of atomic and molecular properties by bouncing things off atoms and molecules. Sometimes the things bounced off the atoms and molecules are photons, sometimes electrons or positrons, and sometimes other atoms and molecules. The ultimate result of the process is always information about the internal structure and interactions of the target atoms and molecules, though.

Given that this kind of science has been going on for decades, now, you might wonder why anybody would still be interested in it. The measurements made in this area are of continued interest to astrophysics, though-- lots of mysteries remain regarding how large clouds of atoms and molecules come together to form stars and planets, for example. There's also a lot of interest in this are for atmospheric science, looking at the interactions of molecules and light or charged particles in the upper atmosphere. The numbers that are produced in traditional AMO contexts serve as crucial inputs for models of astrophysical and atmospheric properties, which help us better understand the planet we live on and the universe we live in.

--Precision Measurement: This almost doesn't deserve to have its own category, as there was only one invited-talk session devoted to precision measurements (though two of the "Hot Topics" talks on the last day were precision measurement talks). There's a distinct enough culture around these topics, though, that I think it's useful to break it out as a separate category.

The goal of precision measurement research is, as the name suggests, to measure things as precisely as possible. Sometimes, this takes the form of standards work-- making ever better atomic clocks, for example-- other times, it's a search for exotic physics. In the prize session on the first day, Gerry Gabrielse described what he does as looking for new physics through high precision, not high energy. In all cases, the cetnral concerns are the measurement of extremely tiny effects, and also all the associated systematic effects that might confuse such a measurement.

These five areas cover most of what's currently interesting in DAMOP. There's considerable overlap between them, of course-- lots of people use ultrafast lasers to study traditional AMO properties, for example, or ultracold atoms as a source for quantum phenomena-- but it makes a useful system for thinking about the various sessions within the meeting.

Over the next week or two, I'll do a series of posts, at least one per topic area, giving a little more detail about what goes on in that sub-sub-field, and highlighting some of the dozens of papers I read in preparation for this talk. If you'd like a tiny taste of what's going on, though, here are my talk slides again:

What's So Interesting About AMO Phyiscs?

View more presentations from Chad Orzel

(Before you take me to task for having too much text on these, these were quite deliberately designed to be text-heavy so they'll be readable on the Internet. I put the SlideShare URL up during the talk, and directed people to look at the slides online for things like the session lists and references.)

drorzel Tue, 06/28/2011 - 06:15

Commanding the Power of Thor...ium: "Wigner Crystals of 229Th for Optical Excitation of the Nuclear Isomer"

drorzel — Tue, 07 Jun 2011 07:58:13 +0000

Commanding the Power of Thor...ium: "Wigner Crystals of 229Th for Optical Excitation of the Nuclear Isomer"

I have to admit, I'm writing this one up partly because it lets me use the title reference. It's a cool little paper, though, demonstrating the lengths that physicists will go to in pursuit of precision measurements.

I'm just going to pretend I didn't see that dorky post title, and ask what this is about. Well, it's about the trapping and laser cooling of thorium ions. They managed to load thorium ions into an ion trap, and use lasers to lower their temperature into the millikelvin range. At such low temperatures, the ions in the trap "crystallize."

So, they've demonstrated that if you get something cold, it forms a solid? Dude, that's not shocking new physics. There are scare quotes around "crystallize" for a reason. They're not forming a real crystal, in large part because we're talking about triply ionized thorium here, so each has a charge of +3 electron charges. They repel each other pretty strongly, and if they weren't held in a trap, they'd fly apart at high speed rather than forming a solid.

The "Wigner crystal" that forms is a regularly spaced arrangements of these ions, each being more or less stationary, separated from all its neighbors because of the electric force between them.They make these really nifty pictures using light scattered by the ions during the cooling process, so that each ion shows up as a dot of light:

Pretty blue dots! That's false color-- the actual light being used is in the infrared, at 984 nm. But yes, it's a pleasing color choice.

Why are there stacks of three pictures? The top picture in each stack shows both isotopes of thorium. For the middle pictures, they block one of the lasers so they only see light from thorium-229, and for the bottom picture, they only see thorium-232. The big picture in part a) is about 200 ions total, with the separation between isotopes having to do with the extra mass. The other pictures show 6, 5, and 4 ions.

Why bother with the tiny little samples? Why not just trap lots and lots of ions? Well, most of the experiments you would like to do with trapped ions work best when you look at a single ion. They trapped 200 ions just to show that they can get lots of them if they want to, but ultimately, they'd like single ions for precision measurements.

You mentioned precision measurements before, too. What's so special about thorium? Well, a little while back, I talked about an experiment using ultra-precise atomic clocks to demonstrate relativistic effects for very small changes in speed or elevation. They're able to see changes in frequency at the level of a few parts in 10¹⁶, which lets them measure tiny effects on time.

These clocks are extremely precise and stable, but still subject to some environmental perturbations, because ultimately, they depend on the energy difference between two states of an orbiting electron, and that electron interacts relatively strongly with the outside world.

Yeah, but what other option do you have? Well, there are the nuclei of atoms. The nucleus of an atom is shielded from a lot of the effects of the environment by the fact that there are all those electrons in a diffuse cloud around the outside of the nucleus-- the electron cloud being something like 10,000 times the size of the nucleus. If you have a stray electric or magnetic field, the electron cloud shifts around a bit, which changes the energy of the electron states, but more or less cancels out the field at the nucleus. This makes nuclear states much less sensitive to perturbations, which is why people talk about using them to make quantum computers.

Yeah, but for the computer, you're just using spin-up and spin-down states. I thought you said that the energy separation of those states depends on what's near them, which is exactly what you don't want for a clock. Right. So the spin states of the nucleus aren't a good idea for a clock. An atomic nucleus, though, has structure of its own, with different arrangements of protons and neutrons having slightly different energies. The energies of those states is set by quantum physics, just like the energies of the electronic states used for ordinary atomic clocks. So, you could make a clock based on the energy difference between two different states of the nucleus of an atom.

Yeah, but when nuclei move between states, they absorb or emit gamma rays. Are you really going to make a clock based on gamma rays? Isn't that more of an Incredible Hulk thing than a Thor thing? Well, yes. Also, it's impossible to manipulate gamma rays cleanly enough to use atomic clock techniques with them.

By a happy coincidence, though, thorium-229 has two nuclear states that are separated by a surprisingly small amount of energy-- just 7.6 electron volts. That corresponds to light in the vacuum ultraviolet region of the spectrum-- around 160 nm wavelength-- which is a little difficult to work with, but nowhere near as difficult to handle as gamma rays would be.

So, the point of all this is to make an even better atomic clock using thorium nuclei? Right. Of course, nobody has ever measured these states exactly, so the first step is to collect a bunch of thorium nuclei, and find out what frequency of light they light to absorb. Hence this paper: trapping and cooling thorium ions is the first step toward measuring these nuclear states precisely, and thus providing another sort of time standard.

Isn't this kind of a lot of work to go to for a new clock? And do we really want to be making clocks out of things that are radioactive? Well, the half life of thorium-229 is several thousand years, so it's not like your clock is going to go "poof" all that often, or be dangerously radioactive. But you underestimate the ambition of physicists interested in making better clocks.

Timekeeping aside, though, there are cool things you could do with a thorium nuclear clock. Specifically, you could make one, and compare the rate at which it ticks to the rate at which an electronic clock like the aluminum ion clock from the relativity experiment ticks.

And this would tell you what? It would tell you whether the constants of nature are really constant, or if they change in time. People look for this sort of change in astronomical sources all the time, and also in laboratory experiments based on comparing different types of clocks. Different types of clocks are sensitive to the constants of nature in different ways, so if you set up two clocks and compare them over a long time, you can tell whether the constants are changing-- if the more sensitive of the two speeds up or slows down significantly, you know something's changing.

A thorium nuclear clock would be radically different from an other type of atomic clock, which ought to allow a really precise test in a relatively short time. That wouldn't necessarily require the clock to work well enough to be able to displace cesium or one of the trapped-ion systems people are making now, and it would be a great probe of new physics.

Which, I'm sure you're going to note smugly, would come from experiments in a laboratory and not a billion-dollar accelerator. Well, yeah. Also, because it would be in a laboratory here on earth, it wouldn't be subject to the same uncertainties as astronomy-based tests, which involve so many variable factors it isn't even funny.

Anyway, that's why this is a worthwhile paper (and was written up in Physics): it's pretty cool in its own right, but the real attraction is that it's the first step toward something really awesome: a nuclear-state-based clock, with the potential to test whether the constants of nature are really constant, or if some exotic new physics is involved in making them change.

OK, that is pretty cool. I'm still not going to forgive you the stupid reference in the title, though. Yeah, well, you can't win 'em all...

C. J. Campbell, A. G. Radnaev, & A. Kuzmich (2011). Wigner Crystals of 229Th for Optical Excitation of the Nuclear Isomer Physical Review Letters, 106 DOI: 10.1103/PhysRevLett.106.223001

drorzel Tue, 06/07/2011 - 03:58

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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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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.

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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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.

Protons: Even Smaller Than We Thought

drorzel — Fri, 09 Jul 2010 08:19:51 +0000

Protons: Even Smaller Than We Thought

The big physics story at the moment is probably the new measurement of the size of the proton, which is reported in this Nature paper (which does not seem to be on the arxiv, alas). This is kind of a hybrid of nuclear and atomic physics, as it's a spectroscopic measurement of a quasi-atom involving an exotic particle produced in an accelerator. In a technical sense, it's a really impressive piece of work, and as a bonus, the result is surprising.

This is worth a little explanation, in the usual Q&A format.

So, what did they do to measure the size of a proton? Can you get rulers that small? They use a particle accelerator to create atoms of "muonic hydrogen," which are just like hydrogen atoms, but with the electron replaced by a muon, an exotic particle that's just like an electron but about 200 times heavier. Once the atoms were created, they used lasers to measure the "Lamb shift," which is the very small energy difference between two levels in hydrogen.

How does that tell you anything about the proton? Aren't the energy levels related to the orbit of the electron? The Lamb shift is an extremely important phenomenon in the history of quantum physics, because the simplest version of quantum theory predicts that these two levels, the 2S and 2P states, ought to have exactly the same energy. The fact that they don't, as discovered by Lamb and Retherford in 1947, was the first clear indication of a need to move beyond the simplest version of quantum theory, and led to the development of Quantum Electro-Dynamics (QED).

The size of the Lamb shift depends on a bunch of factors, but in normal hydrogen is mostly due to modifications of the electron-proton interaction by "virtual particles" in QED. There's a small contribution due to the size of the proton, though, and that contribution gets a lot bigger when you replace the electron with a muon.

How does the size of the proton matter? Isn't it, like, 10,000 times smaller than the electron orbit? The proton is, indeed, really tiny, but its size is not zero. And that makes a difference when you look at how these two states behave.

The two states separated by the Lamb shift are states of different angular momentum-- the 2S state has zero angular momentum, while the 2P state has one unit of angular momentum. This leads to a significant difference in the wavefunctions of the two states, with the 2S state spending much more time close to the proton than the 2P state does.

Angular momentum? I thought that was just about gyroscopes and ice skaters? What's it got to do with atoms? In classical physics, the angular momentum of a moving object depends on two things: how fast it's moving, and how far it is away from the central point. Two objects moving at the same speed can have very different angular momenta, if one is orbiting close in to a central point while the other is much farther out. The object that is farther away has more angular momentum.

The states of electrons in atoms are not really like planetary orbits, but much of the physics carries over in a conceptual way. The 2S state has zero angular momentum, while the 2P state has one unit of angular momentum, and that means that the 2P state is, on average, farther away from the center of the atom than the 2S state (the two states have the same "speed" because they're both 2 states). In fact, if you look at the probability of finding the electron exactly at the center of the atom, where the proton is, the probability is zero for the 2P state, but non-zero for the 2S state.

When you take the finite size of the proton into account, that means that an electron in the 2S state will spend more of its time close enough to the proton to see that it's not a point, but a small sphere of charge (more or less). That changes the interaction energy between the electron and the proton, which in turn changes the total energy of the state. This leads to a shift of the 2S energy compared to the 2P energy, and contributes to the Lamb shift.

So, the Lamb shift is due to the finite size of the proton? I said it contributes to the shift. It's actually a really tiny contribution in hydrogen-- the vast majority of the shift measured by Lamb and Retherford, and in numerous experiments since, is due to other effects. The proton size is part of the shift, though, and is actually one of the main sources of uncertainty in current theoretical calculations of the Lamb shift in hydrogen.

Why is it so small? Becuase, as you noted earlier, the proton is around 10^-15 meters across, while the electron orbits are around 10^-10 meters across. The region where the proton size matters for the interaction is so small that it's almost negligible. It's only because modern spectroscopic methods are so utterly amazing that you can see any contribution to the shift at all.

So this is where the muons come in? Right. A muon is roughly 200 times the mass of an electron, which means its orbit is roughly 200 times smaller than that of an electron. Which leads to a corresponding increase in the size of the proton size contribution. When you replace the electron with a muon, and measure the energy splitting between the 2S and 2P states of this muonic hydrogen, the Lamb shift analogue has a much larger contribution from the proton size. If you know the rest of the effects (and we understand QED pretty well), then you can work out the size of the proton by measuring the size of the shift.

How do they measure the size of the shift? They use laser spectroscopy, and take advantage of the fact that the energy shift is also vastly larger than the Lamb shift in ordinary hydrogen (again, because of the larger mass and smaller orbit). The Lamb shift corresponds to an frequency in the microwave range of the spectrum, but the Lamb shift in muonic hydrogen is in the far infrared range, at around 6 microns. That's an inconvenient wavelength, but one that can be generated with pulsed lasers.

So, they just shine the alser in, and see if it gets absorbed? Actually, they shine the infrared laser in, and look for x-rays coming out. The way it works is that a small fraction of the muonic hydrogen they produce ends up in the 2S state. That state has a ridiculously long lifetime-- limited mostly by the fact that the muons only last two microseconds before they decay-- so once they're in that state, they stick around. A short time after the atoms are created, they blast in a pulse of laser light with its frequency tuned close to the frequency corresponding to the splitting between the 2S and 2P states. The 2P state has a very short lifetime, so any atoms that get excited by the laser will decay very quickly, and emit an x-ray in the process (because the energy difference between the ground state and the 2P state is enormous, thanks to the heavy muon).

When the laser is tuned to exactly the right frequency, they see lots of x-rays from decaying atoms. When it's a little bit off, the number of x-rays drops off dramatically. Then they just need to measure the laser frequency, and they get the Lamb shift directly. And with a bit of math, they can convert that to a measurement of the proton size.

And this is a good measurement? It's a phenomenally good measurement. The uncertainty they report in the size is just 0.00067 femto-meters, compared to 0.0069 femto-meters for the best previous measurement. That's a full order of magnitude better, which is an impressive jump for something this tricky.

What's the catch? The catch is that their result doesn't agree with the previous value. The best previous measurement gives the size as 0.8768 fm, while this measurement gives 0.84184 fm. Even taking the uncertainties into account, these do not agree with each other. The difference is about five times the uncertainty, which just shouldn't happen.

So, protons are way smaller than we thought? Yes and no. This measurement suggests that the size is smaller than that measured in previous experiments, but the difference isn't all that big in absolute terms. And it's possible that there's some effect they haven't accounted for properly in making this measurement.

What sort of effect? Well, if they knew that, they would've accounted for it. There's a fearsome amount of theory going into the conversion from Lamb shift to proton size, so it's possible that something there is a little bit off. It's also possible that there's something wrong experimentally-- this is the first time anybody has ever done laser spectroscopy of muonic hydrogen, so they might've overlooked something.

Or it could be completely new physics.

What's your guess as to the reason? I'm inclined to think it's in the theory somewhere, but that's mostly because I'm an experimentalist by inclination and training. There's an awful lot of theoretical stuff going into the conversion, and it wouldn't surprise me if six months from now, somebody discovers a small tweak that brings this measurement into line with the others, or brings the other ones in line with this measurement. It's a whopping huge error as such things go-- 64 times the uncertainty they think is associated with the theory-- but I wouldn't be too surprised if that turns out to be unduly optimistic. They mention some other determination that gives results more in line with their result, which may point to something.

The experiment that they're doing here is really pretty clean, and there aren't too many factors that need to be accounted for. They seem to have most of those under control, at least from the uncertainty estimates they give for the obvious possible experimental shifts.

"New physics" is obviously the most exciting possibility, here, but it would be really surprising. The physics going into this is really just QED, which is one of the best-tested theories in the history of science. It would be really surprising if QED turned out to be that far wrong, though I'm sure the hep-th arxiv will see a flood of papers proposing one scheme or another for coming up with this kind of result (a new kind of dark-matter particle that couples only to muons, not electrons, or some such).

Whatever it is, it'll be interesting to see how this plays out.

Pohl, R., Antognini, A., Nez, F., Amaro, F., Biraben, F., Cardoso, J., Covita, D., Dax, A., Dhawan, S., Fernandes, L., Giesen, A., Graf, T., HÃ¤nsch, T., Indelicato, P., Julien, L., Kao, C., Knowles, P., Le Bigot, E., Liu, Y., Lopes, J., Ludhova, L., Monteiro, C., Mulhauser, F., Nebel, T., Rabinowitz, P., dos Santos, J., Schaller, L., Schuhmann, K., Schwob, C., Taqqu, D., Veloso, J., & Kottmann, F. (2010). The size of the proton Nature, 466 (7303), 213-216 DOI: 10.1038/nature09250

drorzel Fri, 07/09/2010 - 04:19

Tags

precision measurement

proton

quantum electrodynamics

Quantum Physics

Science

Physics

One thing I could not figure out: what is the size of the proton compared to when it is declared âsmallerâ? the same measurement done previously, or the expected theoretical result, or to a completely different definition and measurement of the âsizeâ of the proton?

(The last option would disturb me less, sizes of complicated objects are ambiguous things, and could very well be probe-dependent.)

The key point in the finite size contribution to the Lamb shift is not just that the lepton spends time close to the proton, but that it spends time inside the proton. Inside the proton, the proton's electric field weakens, and so leptons that can penetrate the proton are slightly less strongly bound than they would be by a point charge.

People have been doing measurements like this for quite some time, and the precision is consistently impressive. However, there is usually substantial disagreement between results. While the experiments tend to be interpreted in a model that considers the proton to be basically a uniform ball of charge (sometimes plus some corrections), the large discrepancies suggest that such a model is insufficient, even at very low atomic energies.

Thanks for this excellent summary :-)

(Seems you forgot to close a bold-face tag somewhere)

More not-so-well-informed commentary:

I spent a while yesterday sifting through the papers they cite, but I'm still trying to wrap my head around the sizes of various corrections. For instance, there's a fair amount of literature on how the proton polarizability affects the Lamb shift. But the discrepancy they find is huge, not just in statistical significance but in absolute terms -- 4% -- so my initial thought it's hard to deconvolve the effects of other QCD corrections (polarizability, vacuum polarization) doesn't seem right. Those effects are smaller. If there's a problem in the theory it seems like it has to be in one of the easier parts of the theory.

My guess is that this experiment is right and the old experiments on ordinary hydrogen got their error bars wrong. (The e-p scattering experiments are even fishier, since they work in regime where the charge radius times momentum is order 1, so disentangling the different terms in the form factor is difficult.)

There's almost no room for new physics to explain this.

This post is just one "bunnies made of CHEEESE?" away from being a conversation with your dog. Which is to say, interesting, easy to read and very informative.

Moshe: they're all measurements of the proton charge radius (i.e., the EM form factor is F(q^2) = 1 - q^2 /6 + O(q^4) and they're extracting the coefficient). The discrepancy is between this measurement and previous measurements (all of which are much less precise). The preferred value that CODATA tabulated, which disagrees by 5 sigma, is mostly based on measurements of ordinary hydrogen, where it's understandably difficult to see the effect of the charge radius, since the electron's orbit is so big. There are also e-p scattering results that give a value 3 sigma higher.

Oops, I tried to use angle brackets in HTML and didn't preview. Trying again:

The EM form factor is 1 - q^2 /6 + O(q^4) and they're extracting the coefficient.

That time I previewed! And it looked fine! And then when it posted it doesn't. Weird.

Dropping the angle brackets:

The EM form factor is 1 - r^2 q^2 /6 + O(q^4) and they're extracting the r^2 coefficient.

Please excuse my biologist's perspective here, but ...

The anthropic fine tuning argument is usually posed as "If the fundamental constants were even slightly off from what we observe, then universe as we know it couldn't exist."

Doesn't the fact that we could have 4% slop in the size of the proton, yet still have a standard theory that works so well for so many things, mean that all of the shouting about anthropic fine tuning is utterly wrong?

This is what I get for writing these things at 11pm. The first "close to the proton" ought to be "close to and even inside the proton."

The anthropic fine tuning argument is usually posed as "If the fundamental constants were even slightly off from what we observe, then universe as we know it couldn't exist."

No.
The fundamental constants that people talk about when they talk about "fine-tuning" are typically dimensionless ratios of other constants-- the ratio of proton to electron masses, or the ratio of the electron charge, Planck's constant and the speed of light known as the "fine structure constant." Small changes in these would lead to enormous changes in the structure of atoms and nuclei, with disastrous consequences for (our sort of) life.

The size of the proton is not a fundamental constant in this category. It almost never comes up (note that Moshe, who is a terrifically smart particle theorist, isn't even sure what's meant by the term-- that's how unimportant it is in the grand scheme of things), and in the limited number of situations where it does matter, it leads to tiny, tiny shifts that only turn up in precision measurements.

It is a property of a fundamental(-ish) particle, but not one that enters into the fine-tuning arguments. Thus, uncertainty in the proton charge radius doesn't affect the fine-tuning argument at all.

While the experiments tend to be interpreted in a model that considers the proton to be basically a uniform ball of charge (sometimes plus some corrections), the large discrepancies suggest that such a model is insufficient, even at very low atomic energies.

Admittedly, I haven't studied the theory behind this experiment in any detail, but I'm guessing that they don't actually assume a uniform sphere. More likely they assume a spherically symmetric (or at least symmetric when time-averaged) charge distribution and calculate a moment of the distribution. That moment can be used to infer a length scale (probably a Radius of Gyration, in formal terms) but that's a bit different from the radius of a uniform sphere. That's how perturbation calculations usually work.

@Alex -- Mathematically, it doesn't really matter whether you actually assume a uniform ball of charge, but that's usually how the people doing these experiments describe their results to general physics audiences. The form factor that they actually end up studying is sketched out over the course of three comments above. However, when they quote a radius, I believe that is the radius of a uniformly charged sphere that has the correct form factor.

I suppose the key point is not that the measurement of proton "size" has much intrinsic significance, but that the apparent discrepancy may reveal a problem with QED. At present, this seems like the least likely outcome.

With regard to fine-tuning, there are also many other absolute physical constants upon whose values the existence of (our sort of) life is rather insensitive. In fact, without wanting to derail the thread, the distribution of absolute fundamental constants, and therefore any dimensionless combination of them, can be shown to follow a 1/f law irrespective of any system of units. This is exactly what would be expected for a set of "fundamental" numbers that are unrelated to each other - they are randomly distributed.

One part of this does not surprise me. Measurements of the charge distribution of the proton were done fairly crudely by the highest energy physics community when those measurements were in the first-ever win-a-Nobel territory at SLAC. It is rarely fashionable to improve on measurements like that, but I'm pretty sure that the Bates and Jefferson labs did runs with polarized beams and H targets at electron energies that probe well below the sizes seen in this experiment. Pretty sure, but not confident.

So is this a claim that the electron scattering data are wrong because the electron alters the proton (quark) charge distribution? If so, they need to explain how they modeled the larger effect of a muon on the quark distribution.

Or is it a claim that there is a systematic error in multiple sets of experimental data taken at different laboratories, perhaps because those experiments were done casually without great attention to that sort of detail?

I haven't looked at the paper, so I don't know how they parametrized the proton charge distribution for their calculation and/or if it agrees in detail with what is known from experiments done by the particle and nuclear physics community. That would be the first question I would ask. There are some commonly used shapes that only agree on the first non-trivial term in the q^2 series.

@10: The "radius of the proton" normally means the rms radius of the charge distribution determined from the electric form factor. Qualifiers are used when discussing the radius determined from the magnetic form factor.

I should have had one other item on my list above, which is the possibility that the e-p measurements are OK (meaning consistent) but sloppy and the real discrepancy is between the atomic H and muonic H calculations of the radius, perhaps magnified by the imprecision of the charge form factor. The mention of new e-p experiments (or analysis of old ones that were never published?) suggests it might be a combination of all of these.

Does the energy state of the proton contribute in any way to the measurement, or more specifically to the error margin?

I think this is closest to the real story. The reference to other experiments/ theory is this sentence:

"Dispersion analysis of the nucleon form factors has recently32 also produced smaller values of rpâââ[0.822...0.852]âfm, in agreement with our accurate value."

which points to this paper which appears to be some sort of re-analysis of other people's scattering data. The abstract contains the following:

"We simultaneously analyze the world data for all four form factors in both the spacelike and timelike regions and generally find good agreement with the data. We also extract the nucleon radii and the ÏNN coupling constants. For the radii, we generally find good agreement with other determinations with the exception of the electric charge radius of the proton, which comes out smaller."

It's not a completely solid explanation-- the Lamb shift measurements in ordinary hydrogen are the culmination of a series of many steadily improving measurements over a period of many years, so saying "well, those should have bigger error bars" isn't a trivial matter. The experiments are really pretty solid (I know some people who did a Lamb shift measurement, and they were very careful and thorough). It's possible that there's some factor in the theoretical calculation used to convert from Lamb shift to proton radius in those measurements, but those calculations are fairly central to QED, and it would be pretty surprising for them to be that far wrong.

But as improbable as that may be, that may well be more likely than new physics at the necessary level to explain this discrepancy.

This statement on the blog is quantum mechanically incorrect: "...the 2P state is, on average, farther away from the center of the atom than the 2S state." In fact, it is the reverse (from a semi-classical point of view, one would say that the orbit is becoming more circular as the angular momentum increases).

One clarification question -- you cite two numbers. The current study, with muons, comes up with a size of 0.84184Â±0.00067 fm. Previous studies come up with a size of 0.8768Â±0.0069 fm. Those previous studies -- they were using standard electron Hydrogen atoms, or other methods? Or are those previous studies making the same measurement, with muonic Hydrogen?

I don't doubt the accuracy of the hydrogen Lamb shift measurement, just of the inferred value of the charge radius extracted from it.

It's possible that there's some factor in the theoretical calculation used to convert from Lamb shift to proton radius in those measurements, but those calculations are fairly central to QED, and it would be pretty surprising for them to be that far wrong.

It's not so clear to me; there are a lot of obscure higher-order effects in the literature that I don't trust to be so well-understood, but this does look awfully large to be attributed to any of those. On the other hand, ordinary hydrogen really isn't very sensitive to the proton size (the proton radius divided by the Bohr radius is something like 10^-5), so pretty small corrections can matter.

Another issue that I'm not sure about is that the proton electric form factor is actually a little ill-defined since the photon is massless; in the limit where you turn off the QED gauge coupling, it's a well-defined quantity (which in principle can be computed by lattice QCD, though the latest numbers I've found have error bars too big to be of interest here), but there are IR divergences in general. Presumably there's a standard way of dealing with this, but I haven't dug it up yet.

The prior studies that got the larger value are studies of normal hydrogen, not muonic hydrogen. They're using laser spectroscopy of ordinary atoms, with no accelerators needed.

Thanks onymous, your comment and the rest of the discussion make it clear what are those earlier results implicit in the original discussion, and their relations to the new measurement.

Because muons are smaller because they are more massive, and because they spend more time inside the proton, doesn't the negative charge of the muon while it is inside the proton make the charge radius of the proton smaller (while the muon is inside it)?

Sorry I didn't have time to read all the comments but I note and query: isn't the size of the proton more than an abstraction about things like Lamb shift would show, in the sense of being somewhat literally for packing purposes such as density of neutron stars? (And to a more subtle extent, cross-section for absorptions etc?) It is at least somewhat like the effective physical radii of atoms and molecules, no?

Was the effect, which has served for spectroscopic determination of deuterium in 1932 considered?

http://www.marts100.com/deuterium.htm

While in grad school, I drew a short lived comic strip about a sheep that drove a race-car called "Lamb Shift: Racing Sheep".

It wasn't funny then either.

I am puzzled a bit by the error bar for the new, smaller rms proton charge radius claimed in the paper. Actually, this radius r is calculated from the relation

ÎE_Lamb = E_0 â A rÂ² + B rÂ³,

where ÎE_Lamb is the measured Lamb shift, and the constants E_0, A, and B result from QED calculations. There is a freely available supplement to the paper which explains how these constants have been obtained, and which QED terms have been included in the calculation.

Now, while the paper discusses the error bars of the measured ÎE_Lamb and of the constant E_0 (which has error bars due to uncertainties by approximations etc...), the constants A and B seem to be used without error bars. But, actually, the supplement quotes two calculations of A which differ at the per-mille level, so there still seems to be a corresponding ambiguity in the calculations.

Now, I am wondering, how can one ignore this uncertainty (it seems to be ignored in the paper, at least), which is one order of magnitude larger than the uncertainties in ÎE_Lamb and E_0, in the calculation of r?

What am I missing here?

The Tau, Muon and electron all operate in a dynamic parameter, so that each time you use these to measure the proton, it should not be the same (now that we have the ability to measure at such a critical value)The dynamics of the Leptons should create a variable within parameters that we now are able to see.

It looks like there will be a high and low value to the proton using the method of laser spectroscopy, what may be needed is more confinement of the leptons utilised.

But then what do I know.

Question from a dopeydollop who don't know much but is interested in this and wants to know more.

According to the searches I've done so far the proton size can be calculated from the Rydberg constant.Is this correct are, there any equations that give the proton size and if there are where can I search to find these equations?Thanks.

@Tex: The anthropic fine tuning argument is usually posed as "If the fundamental constants were even slightly off from what we observe, then universe as we know it couldn't exist."

I *really* don't like that phrasing. A better one is "If the fundamental constants were even slightly off from what we observe, then we wouldn't be here to observe them."

Universes that don't have physical constants enabling conscious observers to evolve will never be witnessed by conscious observers. And any conscious observers evolve in a universe that permits them will be precisely those possible under whatever the extent constants are.

IOW: It isn't about how fine tuned the hole is to the puddle but how the puddle fills whatever hole happens to exist.

@Jim (#18): OK, technically you're correct, if you compute [r] (brackets stand for expectation value) for Psi_200 and Psi_210, you get 6a_0 for the 2S state and 5a_0 for the 2P state (assuming I did my arithmetic correctly). But if you're only interested in time spent near the proton, you don't want to let the radial integral go to infinity. If you cut it off at some small value, say a_0, then you get [r]_2S >> [r]_2P, which was the point.

Oops, that last bit should read P(r> P(r

Argh character problems again: "the probability for r less than a_0 in the 2S state is much bigger than the probability for r less than a_0 in the 2P state"

@17: Thanks for looking that up in the paper and including the link to reference 32.

That reference is really interesting. The abstract suggests that theoretical (based on decades of non-leptonic scattering data), rather than experimental (that is, a WAG about where to draw the background) treatment of the continuum introduced a non-trivial systematic error in the e-p data. This does not surprise me based on my past experience with (mumble). I'm going to have to go read the entire article.

I suppose the key point is not that the measurement of proton "size" has much intrinsic significance, but that the apparent discrepancy may reveal a problem with QED.

Actually it does. An entire class of energy devices relies on the movement of ions (Batteries, Fuel cells etc) including protons. The fastest moving ions are the protons due to their small size.

Re: Comment #35

Proton mobility in a battery / fuel cell / chemical process has very very very very little to do with the finite size of its charge distribution. It has a lot to do with the electron(s) around it and its mass.

Question: How is the "size" of a proton defined exactly? I was under the impression that all elementary particles are point-size under the Standard Model. However, the proton is not an elementary particle, and is composed of three quarks. So am I correct in thinking that the "size" of a proton is related to the distance between the three quarks? Isn't that a matter of QCD rather than QED?

@Yoni (Re: #31)
It is clear that only S states have non-zero density at the center-of-mass of the nucleus-electron pair(still within the nucleus), and, that within a given electronic level, density sufficiently near the nucleus decreases as angular momentum increases.

It is also interesting to ask at what distance r will a 2S state have the same probability of being within a sphere of radius r as a 2P state. That distance is 1 bohr radius, the most likely distance in the 1S state.

I'm just now getting around to reading this and thought it might be of some interest here.

http://tgd.wippiespace.com/public_html/paddark/shrinkingproton.pdf

From comment#10,

"It is a property of a fundamental(-ish) particle, but not one that enters into the fine-tuning arguments. Thus, uncertainty in the proton charge radius doesn't affect the fine-tuning argument at all."

Just a layman here but, could this have implications for the fine structure constant? I would have thought a smaller charge distribution field would affect the EM coupling strength??

Pears And Apples
Electrons-scattering and muon-Lamb-shift

"Size of a proton?"
Really small. But physicists can't agree on one number.
http://www.sciencenews.org/view/generic/id/67759/title/Size_of_a_proton…

In order to agree on a number, physicists should first agree on the proton's "functional size" they wish to measure.

The obtained electrons-scattering and muon-Lamb-shift sizes may BOTH be right, reflecting two different "functional sizes" of the proton.

Dov Henis
(comments from 22nd century)

"Record number of photons lassoed into a quantum limbo" (Dec 25 2010 comment)
http://www.sciencenews.org/view/generic/id/59217/title/Record_number_of…

Amazing Laser Application 11: Frequency Combs!

drorzel — Wed, 21 Apr 2010 09:55:27 +0000

Amazing Laser Application 11: Frequency Combs!

What's the application? An optical frequency comb is a short-duration pulsed laser whose output can be viewed as a regularly spaced series of different frequencies. If the pulses are short enough, this can span the entire visible spectrum, giving a "comb" of colored lines on a traditional spectrometer. This can be used for a wide variety of applications, from precision time standards to molecular spectroscopy to astronomy.

What problem(s) is it the solution to? 1) "How do I compare this optical frequency standard to a microwave frequency standard?" 2) "How do I calibrate my spectrometer well enough to detect small planets around other stars?" 3) "How can I do precision molecular spectroscopy really quickly?" 4) "How can I do qubit rotations faster in my ion trap quantum computer?" among others.

How does it work? The key idea is that in order to make short pulses of light, mathematically, you need to add together large numbers of waves at different frequencies. I talk about this a little in the book, from which I'll lift this figure:

From bottom to top, this shows a single frequency, the sum of two different frequencies, then three different frequencies, then five. As you can see, adding mroe frequencies gets you a shorter pulse (where the waves are obvious) with a larger gap between pulses.

When you do this with the right sort of laser, you can generate a pulse whose length is given in femtoseconds (10^-15s, or 0.000000000000001s). That kind of ridiculously short length requires an extremely broad range of frequencies to make it up, which can be pictured as a "comb" of lines of different frequencies, corresponding to the different colored lines seen in this figure lifted from the group of Theodor Hänsch, who shared the 2005 Nobel Prize for developing the technique:

The lines of the comb are separated by a frequency that is determined by the repetition rate of the laser, which can be controlled extremely precisely. If the "comb" is broad enough (the technical term is "octave-spanning") it's possible to find high-frequency lines that are at double the frequency of some of the low-frequency lines, which lets you nail down most of the systematic effects that would otherwise plague the measurement. And if you arrange things right, you can get one of the lines to line up with a line from an atomic standard (a rubidium atom, say, or a mercury ion), and lock the frequency of that line to the frequency of the atomic standard to the sort of precision that people expect from atomic clocks-- a few parts in 10¹⁶ or so. That gives you a collection of regularly spaced lines spanning more or less the entire visible spectrum, with all of their frequencies known to fifteen or so digits.

This is an incredible resource for all sorts of physics. For one thing, it gives you a way to make direct comparisons between atomic clocks running in very different regions of the spectrum. This is a huge issue, because atomic clocks based on visible or ultraviolet transitions offer a lot of advantages over traditional microwave clocks when it comes to accuracy, but it's very difficult to get an optical frequency down to something useful in the lab. The frequency comb lets you do that.

It can also be applied to spectroscopy in areas like astronomy. The figure above is from the Hänsch group's experiment using a frequency comb to calibrate a spectrometer for astronomical observations, and we had a very nice talk last week by Dr. Chih-Hao Li, who's doing similar work with Ron Walsworth's group at Harvard. The idea is that the comb gives you a way around one of the limitations in spectroscopy of stars, which is that the calibration of the instruments is difficult, and tends to change over time. That leads to an uncertainty in Doppler shifts measured for astronomical objects. The comb provides a nearly perfect calibration source, with atomic-clock precision over a huge range of wavelengths-- the Walsworth group's tests spanned almost 100nm in wavelength, and they think this could allow them to measure Doppler shifts of stars at levels corresponding to a few centimeters per second. That's about the size of the shift Earth would cause in the Sun's spectrum as we orbit, so that level of precision could allow the detection of Earth-like planets through Doppler shift measurements.

You can also apply the comb directly to spectroscopy, as Haänsch's co-laureate Jan Hall has done in spectroscopic experiments at JILA in Colorado. They use the comb to detect trace amounts of particular gases, based on the way they absorb some lines and not others. (If you click on the picture on the page linked, there's a spiffy animation to go with the press release.)

Even more recently, Chris Monroe used a frequency comb to drive transitions in a trapped ion, which could be a faster way of doing the operations needed for quantum computing, where you often need widely separated frequencies that are controlled with extreme precision.

Frequency comb sources are a relatively new technology, so people are still coming up with amazing things to do with them. It's one of the most exciting areas in AMO physics right now.

Why are lasers essential? The entire comb generation method depends on using a laser. There's absolutely no way to make this sort of source without the laser principle-- it's not just a really bright light, it's a really bright light with very special frequency and phase properties.

Why is it cool? Dude, ultra-precise spectroscopy at essentially any wavelength! Extrasolar Earth-like planets! Fast qubits! What more do you need?

Why isn't it cool enough? Only great big nerds really get excited about ultra-precise spectroscopy and all that other stuff. Sadly, many ordinary people are bereft of the soul needed to appreciate the utter coolness of frequency comb sources.

drorzel Wed, 04/21/2010 - 05:55