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.