Note: This post is my contribution to the third edition of The Giant’s Shoulders, a carnival of blog posts on classic science papers.
One of the most famous statements concerning quantum mechanics, as it relates to the light particles known as photons, was made by the brilliant scientist Paul Dirac in his Quantum Mechanics book1:
“each photon then interferes only with itself. Interference between different photons never occurs.”
This statement is bold and unambiguous: in Dirac’s view, a photon only creates interference patterns by virtue of its own wave function, and wave functions of different photons do not interact.
The statement is bold, unambiguous, often quoted — and wrong! In 1963, Leonard Mandel and G. Magyar of Imperial College disproved this statement2 with a clever and simple experiment and a two-page paper in Nature. I was reminded of this work by a question on my recent post on coherence, and it seemed worth reexploring. Follow me below…
From our earlier discussion of optical coherence, it is perhaps not surprising why Dirac would make such a statement. Interference requires, in essence, that the wave fields being interfered have a definite phase relationship with respect to each other. This phase relationship is usually achieved by dividing a quasi-monochromatic wavefield into two or more parts which are then brought together to interfere. Two independent lasers, however, will fluctuate independently of one another and on average will produce no discernable interference pattern.
Furthermore, it is known that the interference pattern in Young’s double slit experiment appears even when only one photon (or electron) is sent through the slits at a time, seemingly making `multi-photon interference’ irrelevant. A single photon will produce a small spot on a detector, but if one observes the experiment over time as more and more photons appear, the interference pattern appears just as if a continuous beam of light were used! From Wikipedia, we present below some experimental results of Young’s experiment using single electrons:
The gradual appearance of the interference pattern suggests that an individual photon is in some sense interfering with itself. It is easy to make the leap that all interference effects occur within the behavior of a single photon, and that interference of an ‘ordinary’ light field is simply the combination of these patterns.
But can different photons interfere? Let us refer again to a statement I made above: “Two independent lasers, however, will fluctuate independently of one another and on average will produce no discernable interference pattern. ”
One should note the emphasis: “on average”. Let us ignore the particle nature of light and think about the light from the two independent lasers as classical waves. Over a long period of time, two identical lasers will have on average no phase relationship between each other. But each laser has some amount of temporal coherence: over some short period of time, the two lasers appear to be nearly monochromatic, and with a definite phase relationship they should produce an interference pattern. To emphasize this, let me recycle a figure from my coherence post:
The two fields depicted here, one random (in blue) and one monochromatic (in red), have times at which they are in and out of phase. But for significant periods of time, there is a definite phase relationship between the two fields. For instance, for at least two oscillations on either side of the ‘in phase’ peak, the waves remain in step. If we were to only look for interference patterns over that very short period of time, we should be able to see fringes.
This, in essence, is what Magyar and Mandel did experimentally. Two independent ruby lasers (still called ‘optical masers’ at that time: this experiment took place only 3 years after the invention of the laser) serve as sources for the experiment. To quote the paper,
Two light beams from two independent ruby masers are aligned with the help of two adjustable 45º mirrors and superposed on the photocathode of an electronically gated image tube. The tube is magnetically focused and the image produced on the output fluorescent screen is photographed.
The detector, in essence, is a sort of crude television: light illuminating the photocathode releases electrons, which are accelerated to a fluorescent screen, producing a photographable image.
The two lasers are ‘fired’ at the same time; however, they emit their energy randomly in a series of very short pulses, and the pulses from the individual lasers may or may not overlap. Part of each laser field is split off and sent to a coincidence counter, and the detector is only activated when two pulses arrive at the same time. A simplified schematic of the experiment, adapted from the paper, is pictured below:
This experiment is very much like Young’s double slit experiment and, if successful, should produce an interference pattern very much the same. The results from the paper are shown below:
Thanks to the weakness of the fringe pattern and the poor photo reproduction of the era, the photograph is a bit of a Rorschach test of a scientific result. the microphotometer tracing below it, though, is unambiguous: the fields from the two independent lasers produce a fringe pattern!
As we have said, fringes are visible as long as the two fields maintain a definite phase relationship with respect to one another, i.e. as long as they both remain essentially monochromatic. As this is in essence the definition of the coherence time, the two fields will produce a visible interference pattern as long as the pattern is recorded on a time scale short compared to the coherence time.
This experiment was one of many clever experiments done by Leonard Mandel to study the quantum mechanical nature of light. Mandel, until his death in 2001, was one of the founders and leading researchers of this field of quantum optics, which has led into the study of such science fiction-y topics as quantum teleportation, quantum computing, and quantum cryptography. This experiment on interfering independent light fields was a prelude to even more amazing work Mandel would do once he moved to the University of Rochester.
In fact, only four years after the experiment, Mandel, along with R.L. Pfleegor3, would take it a step further: the collaborators demonstrated that interference effects from independent light beams could still be found even when the intensity of the light fields is so low that, with high probability, one photon is absorbed before the next one is emitted by either source! In such a case, one cannot even imagine that the interference is produced by the interference of a pair of photons! An interpretation of these results requires much more quantum mechanical thinking than we have time for in this post. It should be noted, though, that the effect is somewhat analogous to the single-photon Young’s double slit experiment mentioned above.
(Full disclosure: I actually knew Mandel, though not well, while I was a student at the U of R. In fact, I had an office right next door to his.)
**********************
1 P.A.M. Dirac, Quantum Mechanics (Oxford University Press, London, 1958), 4th ed, p. 9.
2 G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature (London) 198 (1963), 255.
3 R.L. Pfleegor and L. Mandel, “Interference of independent photon beams,” Phys. Rev. 159 (1967), 1084.
Skulls in the Stars 
This fragment nagged at my memory, so I dug it out:
The Feynman Lectures on Physics (1964), p. 32–5.
Curses! All those instances of “-8” should have been in superscript.
Blake: No doubt about it: if Feynman were alive, he’d be a kick-ass blogger.
And what do you mean, ’10-8′? ‘Ten to eight’? That makes no sense whatsoever!!! 🙂
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Hi! I was surfing and found your blog post… nice! I love your blog. 🙂 Cheers! Sandra. R.
I was wondering: when you perform such an experiment, can you really be sure that you are not seeing interference of one photon with itself? If you switch one laser off: no interference, which is OK since you know where the photon came from. When both lasers are on, you do not know where a photon comes from, and therefore this photon interferes with itself. So does this experiment really contradict Dirac’s statement?
Now that is even more interesting… The last sentence of the paper you cite as ref [3], is “Surprising as it might seem, the statement of Dirac quoted in the introduction appears to be as appropriate in the context of this experiment as under the more usual conditions of interferometry”.
I would say that according to the authors of [3], Dirac’s statement is bold, unambiguous, often quoted — and possibly correct.
The problem as I see it is that Dirac’s statement is oversimplified, misleading, and almost meaningless in the context of modern quantum optics. As it stands, Dirac’s statement taken by itself cannot be used to predict any of the effects of the experiments described, and his statement can only be applied by interpreting the meaning of the word “photon” beyond what the scientists of Dirac’s era intended.
The situation to me is similar to the wave-particle duality controversy of the past three hundred years. First scientists thought that light was a particle, then a wave, then a particle (photon) with wavelike properties. Does this mean that the statements of the early particle proponents were correct? Only on a superficial level; the real nature of light is way more complicated than those early researchers envisioned.
Found in a google search, thanks for the post and article, very clear!
But I have a question: Is the reason for the interference that what maurizio said in his first post; namely that there is interference because you cannot distinguish between both sources, i.e. they are identical and thus the wavefunction of the events should be added before ‘squaring’?
If so then I wonder about the result of the following experiment:
If you take two lasers, where one has a slightly higher or lower frequency (of only a few hz-khz or so). If these interfere, this would give a time-dependent interference pattern right? in the order of the modified frequency. My question is, would this interfere?
What I just described is a modified case of laser doppler interferometer. In the normal setup (http://en.wikipedia.org/wiki/Laser_Doppler_vibrometer) a laser beam is split into a reference beam and a laser beam which frequency is modified because it is reflected of a moving object (doppler shift), both beams then show a time dependent interference pattern because of the frequency modification (the ‘frequency’ of the interference pattern is dependent on the speed of the moving object, so thats where it is used for). Now if you replace the reference beam by a second laser, instead of splitting the old laser. Do you still see an interference pattern? If so, is the previous description of identical particles or events incorrect?
I hope I made myself a bit clear 🙂
I’ve read somewhere that Dirac’s statement was made when field theory hadn’t come into existence. So in terms of field theory, the modified statement would be that a 2-photon field would never interfere with a 3- or a 4-photon field
Dirac’s statement was made, I believe, in 1933 in his QM book. It seems that field theory was already being investigated at that time, but wasn’t nearly mature enough to have led to a good understanding of its implications.
” the modified statement would be that a 2-photon field would never interfere with a 3- or a 4-photon field”
That’s a good way to put it, especially the emphasis on “the modified statement”! Part of the point I tried to make with this post is that Dirac’s original statement was made in complete ignorance of later QFT developments. In a broad sense, one can reinterpret his statement as being “true”, but such reinterpretations go way beyond what he likely envisioned.
Thank you for the insightful post. I will send the link to students of mine taking a (*very*) introductory quantum optics class. We are covering quantum coherence and I really think that your blog entry will be of great help to their understanding.
Thanks again,
Julian
Glad you liked it, and I hope the class finds it insightful!
Please tell your students to read (anything) with a critical mind… In particular, tell them to consider the title of this article ““Interference between different photons never occurs:” Not! (1963)” in the light of what Mandel and Magyar wrote three years later in ref [3]: “Surprising as it might seem, the statement of Dirac quoted in the introduction appears to be as appropriate in the context of this experiment as under the more usual conditions of interferometry”. Mandel and Magyar understood that their experiment, even in its more refined version produced years later, did not actually contradict Dirac’s statement.
I already raised this point earlier and the author of the blog did not answer it, he just moved the goal post from “The statement is bold, unambiguous, often quoted — and wrong!” to “The problem as I see it is that Dirac’s statement is oversimplified, misleading, and almost meaningless in the context of modern quantum optics.”
The experiment reported here does not disprove Dirac’s statement (as I explained above two years ago), but that does not mean that Dirac’s statement is correct either. Actually, one of the most insightful conclusions to draw from this paper is that interpretation of experimental fact is extremely difficult and that even great physicists can get it wrong.
But in fact ‘two different sources’ is not the same as ‘two different photons’ so this point is incorrect. I hope you will clarify that for your students!
It’s a very interesting article!
I was always intrigued how it seems to be almost impossible to logically explain results of most of the QM experiments, starting with famous Young’s experiment.
I’ve read couple of books about QM, which mostly had descriptions of QM experiments and I’ve tried to logically explain them.
Couple of months ago I think I finally was at the point where I could clearly explain every QM experiment that I’ve heard about.
To do that I’ve developed a theory which among some other things suggested 2 important statements, one of which turned out to be the “famous statement from Paul Dirac”!
Obviously, I’m a novice at QM because today, while I was reading this article, it was the first time when I found out that the Nobel laureate came up to the same conclusion that I did independently of him (obviously he did it about 80 years before me)
When I found that article it gave me additional thought that I really might be onto something!
Anyway, my theory does not only say that “photons can interfere only with themselves”, but it also predicts results for some QM experiments that were not done yet, but which could be done with current level of technology.
My theory says that the results of these possible experiments will be very interesting!
For example, it says that there is an experiment which is a slight modification of a Young’s experiment, that as a result would have an Interference and at the same time it would be clear which of 2 slits photon actually passed on its way.
I’m obviously not a physicist and don’t have connections with the University that can perform such an experiment. And I can’t perform it myself.
So, my question is – who need I talk to regarding that?
Thanks,
Mark
With best technology avilable to date can we obtain the interference pattern using two different light sources?
Certainly — the experiment described in this blog post was done in 1963!
Yes, it is possible and it was also possible in 1963 (although harder). But even nowadays it still proves nothing about Dirac’s statement since the experiment can still be interpreted in a way which does not require one photon to interfere with another photon. By the way: the 1963 experiment involves only electromagnetic waves, there is no indication of what happens at the single photon level.
A great blog indeed, came up as the first link when I typed in the famous quote of Dirac on Google.
Actually the reason for which I started searching this phrase on Google is to look for some insight about ultra-short pulses measurement, which is principally based on interferometry, but this didn’t clear my doubt and it raised further question.
So the experiment by Magyar and Mandel was realized using pulse laser, which in fact consists of a rather huge gain spectrum, so each pulse is made up of many ‘colours’ superposed coherently (please correct me if I’m mistaken). So here are the questions:
1. If only lights of same colour can interfere with each other, how do those different colours in a laser pulse superpose to form a short-pulse in the first place?
2. If indeed each pulse is comprised of different colours, when the two laser pulses interfere, HOW do they interfere? lights of the same colour interfere with each other but not with the others? Are we just concerned with the electric field variation under the envelop of the pulse (if this is the case, then problem solved, just look at the situation classically) ?
3. If I want to look at short pulses quantum mechanically, is each photon in a superposition state of different colours?
I hope someone can clear my doubts, thanks.
As far as I know the answer to your questions would be:
1. The fact that a short pulse can be formed or that a “wave packet” can represent a photon, shows that waves of different frequencies do interfere with each other.
2. Probably the interference between pulses you talk about is between two parts of a single pulse that has been split with a beam splitter.
3. Each photon is indeed a superposition of waves of different frequency which form a wave packet. My understanding is that in order to obtain a very narrow frequency band in a laser, you need to leave it on for a long time. If you have a short pulse, automatically you have a spread of frequencies.
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A very interesting post, thanks! But I do have to point out that these effects are not due to interference between different photons. They’re due to uncertainty about which source emitted each photon. So in fact Dirac was correct. 🙂
Here, by two photons we mean two photons from different source right? Otherwise,
two photons from same source would obviously interefere as they are coherent.