Watching Photons Interfere: "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer"

ResearchBlogging.orgIt's been a long and brutally busy week here, so I really ought to just take a day off from blogging. But there's a new paper in Science on quantum physics that's just too good to pass up, so here's a ReasearchBlogging post to close out the week.

Aw, c'mon, dude, I'm tired. What's so cool about this paper that it can't wait until next week? Well, the title kind of says it all: they measured the average trajectories of single photons passing through a double-slit apparatus. By making lots of repeated weak measurements at different positions behind the slits, they could reconstruct the average trajectories followed by photons on their way to form the interference pattern. They look like this:


Whoa! That got my attention. So, like, these guys are going to get a Nobel, right? What do you mean?

Well, they've measured definite positions and momenta for photons in a double-slit experiment. Which means they must've proved orthodox quantum mechanics wrong, because you've always said that quantum particles don't have a well-defined position and momentum. And if orthodox quantum physics is wrong, that's got to be good for some dynamite money, right? Not so fast. What I said, and what orthodox quantum physics tells us, is that a quantum particle like a photon of light doesn't have a well-defined instantaneous position and momentum. You can perfectly well construct an average position and momentum for a quantum particle, though, by making lots of measurements of identically prepared systems. If you string a whole bunch of those average measurements together, you can construct an average trajectory, which is what they did here.

They haven't done anything to prove orthodox quantum mechanics wrong, though I can predict with confidence that there will be at least one media report about this that is so badly written that it implies that they did. In reality, though, their measurements are completely in accord with ordinary quantum theory.

Yeah? Then how did they manage to measure both the position and momentum without destroying the interference pattern? They made use of an idea called "weak measurement," which is more or less what it sounds like. If you set up a situation where you measure the exact position or momentum of a quantum particle, you lose all ability to measure the other of those two quantities, and destroy your interference pattern. That sort of measurement won't allow you to reconstruct these kinds of trajectories.

If you set your experiment up in such a way that you only get a little bit of information about either the position or momentum of a single quantum particle, though, you only disturb the other quantity by a tiny bit, which means you can go ahead and measure it. This doesn't let you say what the exact position and momentum of a single photon is, but you can measure a fairly exact position with a tiny bit of information about the momentum. If you repeat that many times, you can determine the average value of the momentum at a particular position without upsetting the trajectory.

How do you only measure a tiny bit of the momentum? Isn't that a "little bit pregnant" sort of contradiction? The system they used for this is really ingenious: they use the photon polarization as a partial indicator of the momentum. They send their original photons in in a well-defined polarization state, then pass them through a calcite crystal. Calcite is a "birefringent" material, which changes the polarization by a small amount depending on the amount of material the photon passes through.

Photons that enter the calcite perpendicular to the surface pass straight through, and travel a distance equal to the thickness of the calcite. Photons that enter at a shallower angle follow a longer path through the calcite (think of it like cutting a loaf of French bread on the bias-- the angle-cut pieces are longer than the thickness of the loaf), and thus experience a greater change in polarization. The polarization of an individual photon then depends on the angle it took through the calcite, which tells you the direction of its momentum. The magnitude of the momentum is determined by the wavelength, which is the same for all the photons, so this gives you the information you need for the trajectory.

So, you measure the polarization, and you know the momentum? Sort of. You see, you can't really measure the polarization of a single photon-- when you send it into a polarizer, it either makes it through or doesn't, and that's all you can say. If you want to know the polarization, you need to measure a whole bunch of photons, which lets you determine the probability of transmission, which then tells you the exact polarization.

So, the polarization of each individual photon is correlated with its momentum, but in a way that only lets you get a tiny bit of information out of a single photon. This is a weak measurement of the momentum, and that doesn't perturb the quantum state of the particle by enough to destroy the interference pattern. If you measure a whole bunch of photons, you can reconstruct the average momentum of all the light at a particular position, but that doesn't necessarily tell you anything about the momentum of an individual photon detected at that position.

i-d59a4ba11840b3b69b9a54fb24607b63-photon_positions_momenta.pngThat sounds really complicated. Really clever, but really complicated. It is. It's especially clever because they came up with a nice way to get a cross-section of all the momenta of photons along a line across the interference pattern: they use a set of three lenses to create an image of the light pattern at a particular distance behind the slits on a CCD camera. Just before the camera, though, they insert a special polarization-dependent optic that shifts two different polarization components in the vertical direction (that is, perpendicular to a line drawn between the two slits)-- one polarization shifts up, and the other shifts down. This gives two versions of the intensity pattern, one right above the other, and by comparing the relative brightness of two pixels in a vertical line, they can determine the average polarization of the light at that horizontal position. When they repeat that for all the horizontal pixels, they can make an intensity and momentum plot like the long figure at right.

That's a pretty complicated figure, dude. This is gonna need some unpacking. Yeah, there's a lot going on in this one. The four parts of this figure plot two different things for each of four different distances behind the slits, with the distance increasing as you go down.

The top sub-graph in each lettered part of the figure just shows the total intensity of the light (red is one polarization, blue the other). You can see the development of the interference pattern in these graphs as you gown down the line: at the top, there are just two lumps, corresponding to the two photons that went through each slit. As you move down, those lumps widen out and overlap, and eventually form a complicated interference pattern in the last graph.

The much scarier looking sub-graphs with all the black points are the measured momentum for each position, with positive values being directed upwards (in the trajectory plot at the top of this post) and negative values directed downwards. These are a little noisy, but you can see a clear pattern. The magenta line is a sort of smoothed-out version of the momentum distribution, done by basically requiring that the total number of photons at one slice through the pattern be the same as the total number in the previous slice.

And each of these graphs represents a whole bunch of detected photons? Exactly. For each position, they recorded an image for 15s, which corresponded to about 31,000 photons. Those photons are sent in one at a time-- they did an antibunching experiment to confirm that they're really only sending single photons into the apparatus at a time.

That seems like it would take kind of a long time, doesn't it? Yes, but not nearly as long as it would take if they didn't have the clever polarization-shifter measurement trick, and had to scan a single-photon detector across the pattern.

Good point. So, how do they get from the messy black curves to the nice set of trajectories at the top of the post? Well, those messy black curves give you the direction of the average momentum at each pixel position across the interference pattern. Which basically gives you a lot of little arrows pointing along the direction of the average photon trajectory passing through that horizontal pixel at that distance from the slits. You just set all these sets of arrows next to one another, and draw lines connecting them.

I bet it took quite a while to draw all those lines. They must have some grad students with really steady hands. I think they probably used a computer for the data analysis. It is the century of the anchovy 21st century, you know.

Good point. So, are you sure this doesn't disprove orthodox quantum mechanics? Because those trajectories up top look a whole lot like a picture I saw in an article about Bohm's hidden variable version of quantum mechanics. In the Bohmian picture, these trajectories would be the absolute and true trajectory of the photons passing through the apparatus. In the Bohmian approach, all quantum particles have a well-defined position and momentum at all times, but we're not able to track it directly because the uncertainty in the initial position and momentum prevents us from selefting a single trajectory to follow on repeated measurements.

The more orthodox approach to quantum mechanics holds that the photons do not have well-defined position and momentum before they are detected at a particular position or with a particular momentum. In this version, the particular results of a given measurement of position or momentum is picked at the instant of measurement from a probability distribution determined from the wavefunction at that position at that time. If you repeat this process lots of times, you'll get a different position and momentum every time, but those values will follow a particular pattern. If you average together a whole slew of these measurements, you can come up with an average momentum and average position, which is what they've done here.

When you do that, the result is a set of average trajectories that look exactly like the actual trajectories in the Bohmian picture. So, this experiment would produce exactly the same results, no matter what interpretation of quantum mechanics you favor. In some sense, the only difference between the models is in when you do the averaging: In the Bohmian picture, you take an average because you start with a distribution over all the possible starting positions and momenta, even though each particle follows a well-defined path at all times. In the more orthodox interpretations, you take an average because the final position and momentum that you measure is chosen from a rage of possible values determined from a probability distribution, and the only way to find probabilities is by taking averages.

Any way you look at it, though, you expect trajectories that look exactly like this.

So, no Nobel for the authors, then? As cool as that would be (the PI, Aephraim Steinberg, is a friend from my days at NIST), they shouldn't go booking flights to Stockholm just yet. Unless, you know, they really want to vacation in Sweden.

This is an extremely cool example of the art of experimental physics, and a spectacular demonstration of the power of weak measurements, but it's not that revolutionary. Though, as I said above, I confidently predict that there will be no shortage of crazy people trying to claim this as conclusive proof for their particular favorite interpretation of quantum theory.

(Which is probably appropriate, as Aephraim's Ph.D. thesis research involved "superluminal" propagation of light, which has spawned no end of cranks claiming that Special Relativity has been overthrown. If he can find a really clever test of General Relativity to do, he can complete the trifecta of modern physics kookery.)

So, anyway, was that worth staying awake through Friday?

Yeah, that was pretty cool. Thanks. Now can we call it a week? Yeah, that's about enough for me, too. Stick a fork in this week, and I'm outta here.

Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, & Aephraim M. Steinberg (2011). Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer Science, 332 (6034), 1179-1173 : 10.1126/science.1202218

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Still it is notable that Bohmian interpretation managed to produce the exact same picture while orthodox interpretations did not.

I don't think they make that claim anywhere. It might be computationally simpler to determine these trajectories in a Bohmian formalism, and they're certainly simpler to interpret, but you would get exactly the same answer from a non-Bohmian analysis.

The relevant line in the paper is: "Single-particle trajectories measured in this fashion reproduce those predicted by the Bohmâde Broglie interpretation of quantum mechanics (8), although the reconstruction is in no way dependent on a choice of interpretation."

Do you know of an or other open preprint for those of us not at institutions that can pay for access to papers like this? (I did a quick search on for the author's name, and didn't find this paper.)

Thanks, I'd seen news stories about this that didn't have enough info but wasn't sure I actually wanted to go through and read the paper. This summary was just right.

Compare the Afshar experiment, which supporters claim shows in a single instance which way the photon "went", despite an interference pattern still being evident. I think that instead, in the AE there is a superposition of waves in two directions past the wires placed within the dark fringes. Then detectors aimed in different directions "pick" or collapse (or ...) one of these, and that "seems" to be where the photon came from. But it really didn't follow that unique path all along, it's just an illusion cause by collapse. However, that we can even get a measured direction in the presence of interference, shows that intuitions about such things can be misleading.

Thank you!
My friends are all emailing me the calcite article, claiming something revolutionary and I just say "cool" but there's nothing fundamentally new here (average momentum and position)
New approaches to weak measurements are always cool, but some people go crazy when they happen.

Good blog!!

By Anonymous (not verified) on 03 Jun 2011 #permalink

Bohm? These are photons--ie, relativistic particles. Bohmian mechanics is a total disaster outside thr nonrelativistic regime.

They can book their tickets to Stockholm when they figure out why the photons take those trajectories.

By George P Burdell (not verified) on 03 Jun 2011 #permalink

Thanks, could you elaborate "by comparing the relative brightness of two pixels in a vertical line, they can determine the average polarization of the light at that horizontal position" for single event?
There is only one polarizer, so we can just assume that they observe interference of single polarized photons (?)

So single photon can excite two pixels at once? But in this way they know momentum while interference of single photon?
Or maybe it excites only single pixel and CCD can distinguish 1 +- sin(phi(kx)) photon energy, but the original photon had concrete single wavelength - what's about energy conservation?

Hi Matt,

âBohm? These are photons--ie, relativistic particles. Bohmian mechanics is a total disaster outside thr nonrelativistic regimeâ

If it looks like an ostrich, swims like and ostrich and sounds like an ostrich, what should we suppose it should be? :-)

Beables For Quantum Field Theory

Bohmian Mechanics and Field Theory

A New Pilot-Wave Model For Quantum Field Theory

"The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience"

-Albert Einstein



Weak measurements so far have been a way to trade off a little about complementary features like position and momentum, within the total bounds of the currently accepted range of what we can know about a single particle. The current experiment is a wonderful example of that process. It would be nice to use something similar to "map" a wave function instead of just making binary tests. Perhaps repeated weak-type interactions could accomplish that, for example repeated passes of a photon through a half-wave plate to increment little bits of spin transfer. At name link I explain a program for doing that, and ask whether we could learn more about a photon's polarization state than currently deemed possible. Even if that can't be done, the example is interesting for study.
PS: Something went wrong with my attempted diagram image file for that, am working on it.

[Yeah, "Neil B" and figure looks better now]

Ok - I've found it - the exposure time is 15s (about 31000 photons), but there is no problem to distinguish polarizations because the beam displacer seams to work in y direction - so they probably get two vertical interference patterns (shifted by 2mm) and for each x, the difference of intensity allows to calculate the average kx.
In such case it's not a good argument that they maintain the corpuscular nature ...

Hmmmm... I'd be curious how the weak measurement method could be applied to entanglement/teleportation and neuroquantology.

After this experiment, Bohmian trajectories should no longer be thought of as "hidden variables". As I explain in more detail in my blog
from an experimental point of view, Bohmian trajectories are not more "hidden" than the wave function.

By Hrvoje Nikolic (not verified) on 06 Jun 2011 #permalink

Matt, your comment that it is not "Bohm" because photons are relativistic is irrelevant here, for at least two reasons.

First, it is a matter of time when a similar experiment will be done with nonrelativistic electrons.

Second, there IS a relativistic variant of Bohmian mechanics with particle trajectories. See e.g.

By Hrvoje Nikolic (not verified) on 06 Jun 2011 #permalink

Hrvoje, certain single-particle wave-functions can be observed, for example, in the formation of Bose-Einsten condensation of bosonic particles in the ground state wave-function, thereby creating a "matter wave". Another similar example is the BCS condensate wave-function of a superconductor. Thus, one can claim atleast this class of QM wave-functions do have more experimental reality than Bohmian trajectories, which have never been observed for a single particle.

I'm just a guy that has always been interested in science. I am also a guy that pays careful attention to the use of language. I am also aware that science does not always use our language in the usual way.

That having been said I have always been bothered about the explanation of Young's two slit, of which this appears to be one of the myriad of variations, that light is both a particle and a wave.

Because I pay attention to language I wondered if that was not an linguistic error. Would it not be more correct to say that light is composed of individual discrete particles, upon which the experiment here seems to depend, that normally travels in packets called quanta, which themselves take on in motion a wave formation?

But here the measurements are of individual photons, if I am not mistaken. Further this experiment appears to be saying that the wave data they have discerned is an average, because you cannot directly determine position and direction at the same time, and further that when you put together the data of all the measurements of all the photons they present the usual Young's interference pattern.

In this world of relativistic physics it might be small potatoes but does this experiment, and reading some of the other comments other experiments, not require a correction to the statement, and therefore concept taught to every school child (At least some seventy years ago)that light is BOTH a particle and a wave? Would it not be more accurate to say as I did earlier that light is made up of individual discrete particles that travel in patterns that when measured or viewed together appear in wave form?

Again, linguistically, or more accurately because language and concept are the same thing, does this experiment not go toward destroying the assertion of quantum physicists that you cannot know position and momentum of a relativistic particle at the same time?

Is it not true that the outcome of the weak measurement is in fact an imprecise measure, but nonetheless real measure of the exact position of a particle at any one moment? Is not the entire history of our scientific conception of our universe not that, measuring particles or galaxies, of ever closer refinement of measure and conception?

Jack Jersawitz

By Jack Jersawitz (not verified) on 06 Jun 2011 #permalink

Ravi, thank you for your remark on Bose-Einstein and BCS condensates. However, as far as I understand them, such observed condenstates are macroscopic objects involving MANY particles. So it's not really true that the single-particle wave function can be directly observed.

By Hrvoje Nikolic (not verified) on 07 Jun 2011 #permalink

Ben dil dikkat Ãünkü o bir dil hata olup olmadıÄını merak ettim. daha deneme burada normalde kendilerini hareket halinde bir dalga oluÅumu almak quanta adı verilen paketlerin içinde seyahat ki, baÄlı görünüyor bunun üzerine o ıÅık, bireysel ayrık parçalardan oluÅmuÅtur söylemek doÄru olmaz mıydı?

There have been a ton of blogs now stating that this is evidence that Bohmian trajectories are the accurate picture of reality. However, as Chad stated, Bohmian mech and wave-function collapse interpretations would agree on the results.

I think a far more interesting set of tests for Bohmian vs Copenhagen etc. are those involving the Leggett inequalities, which place limits on "realist" interpretations of QM. So far, the results have not been favorable to interpretations that require particles to have definite properites (albeit unknown/unknowable. It looks like we may have to jettison not only locality, but realism as well, however psychogically unsatisfactory that may be. Of course, there are ways to salvage some realist interpreatations, so the jury is still out...

Mike, I thought that things hadn't changed much since the Aspect experiments and variations of same except for technical improvements. Pls. post links about new ones, especially that added conceptual insight or further evidence against locality/realism in principle.

Mike, one should distinguish Bohmian trajectories from Bohmian interpretation. While this experiment certainly confirms that Bohmian trajectories are (in a certain "weak" sense) real, it is definitely not a proof that Bohmian interpretation is right. I have explained it in my blog, a link to which I gave in one of my comments above.

By Hrvoje Nikolic (not verified) on 08 Jun 2011 #permalink

Hi Neil,

The most recent example of a Leggett test is below:

Here's another from nature a few years ago:

Leggett inequalities follow a similar strategy to Bell inequalities by positing a metaphysical relationship and then deriving bounds on correlations. Bell's inequalities test locality, Leggett's inqualities test realism. Both have been found to be violated in experiments. Again, there are ways to get around the obvious implications of the violations, but it requires some theoretical straining (in my opinion)

Thanks, Mike. BTW would you say the excuse of detector inefficiency is by now simply a lost cause (I just can't help puns ...)

ALeyram: the simple popular concept is that the "quanta" are units of interaction energy, not what "travels through space." However, individual photons could be separated by more distance than their coherence length and thus "quanta" in space in effect. I suppose it depends if you consider lumpiness of the wave function distribution in space to allow that characterization. Many photons together spoil and differentiation. However note that even photon number itself is subject to uncertainty, and only some states have a definite number of them.

This reminds me, anyone: we see "photons" as if spherical shells (presumably one coherence length thick) but of course they have an effective "width" too as shown by RH Brown's proxy wave interferometry (& re Twiss/Brown experiments) which was not the usual sort. I always found that odd, I think that a "width" determined by angular diameter of source must be a relational effect involving many photons: how could one photon emitted once in awhile, (interval longer than coherence time) "know" how wide a spot others came from or be coming from later?

BTW CL is physically real as a spatial distribution: self-interference of sporadic photons quits when the phase difference exceeds it. I doubt this issue affected the experiment noted in the post.

PS anyone interested in continued debate about Born's Rule can go to my blog, per OP wish to discontinue at UP.

A comment on Leggett inequalities:
QM and experiments violate them, which excludes a wide CLASS of "reality" theories but not all "reality" theories. More precisely, this excludes only non-contextual theories. But Bohmian mechanics is contextual, so it is compatible with QM and experiments.

By Hrvoje Nikolic (not verified) on 08 Jun 2011 #permalink


Thanks for the clarification -- Leggett models are only ONE class of "realist" models. However, I recently corresponded with one of the main investigators of the 2010 study regarding the results and they confirmed that the results are evidence against particles having well defined properties, to quote:

"...our data does not agree with Leggett's [premises], i.e. in particular that the individual particles cannot have well-defined properties."

Since Bohmian mechanics requires that particles have a unique position (albeit unknowable), I would say that a violation of Leggett's inequaltiy applies to this. From what I know of the concept of contextuality (not much), it states that the results of measurements depend on all other measurements being done on the system. However, in that case, we cannot say a particle has a particular property at each point in time, but only that the system is in some particular configuration that is linked by nonlocal correlations.

If that is the case, the contextual theories may be called "realist" in some sense, but not in the typical sense that we understand it, (i.e. that each particle has a unique trajectory in space independent of what we do)

Somethings wrong with Figure 1. Not a single photon crosses the center line.

By s. poultney (not verified) on 12 Jun 2011 #permalink

Somethings wrong with Figure 1. Not a single photon crosses the center line.

By s. poultney (not verified) on 12 Jun 2011 #permalink

Mike, thank you for your comments.

But I must say that I never understood the view that reality should be independent on what we do.

By Hrvoje Nikolic (not verified) on 13 Jun 2011 #permalink

S. Poultney, the crossing you observed should be attributed to an experimental error. (As you know, any experiment has an error, even if not shown explicitly as in the picture they have drawn.)

By Hrvoje Nikolic (not verified) on 13 Jun 2011 #permalink

Somethings wrong with Figure 1. Not a single photon crosses the center line.

There's nothing wrong with the figure. That's exactly the result you expect for these average trajectories, whether you calculate them by Bohmian or more traditional means.

To the extent that it makes any sense to talk about a single photon having a trajectory (which isn't very much), you might expect to see individual photons crossing the center line. The average of all the photon trajectories starting in a given slit, though, will stay on one side of that line.