How Big Is a Photon? - Exploring Interference Experiments

[Grelbr42]

TL;DR Summary

YouTube video reports on an experiment of "single photon interference" and gives an explanation I don't understand

This YouTube video, with the same title I have given this thread, reports on an experiment.



He sets up an interference experiment. The light source is a HeNe laser. The light passes through a beam splitter then through two paths. The shorter path being about 0.26 meters, the long one about 1.3 meters. The light returns to a detector. The light is reduced to an intensity such that there should be an average of less than one photon at a time in the apparatus. He estimates 1/250th of a photon in the system at a time.

He still observes interference when both paths are open, but not when either is closed. The different path lengths are roughly 1.6 million wavelengths different.

Later in the vid he provides an explanation. I do not understand his explanation. And I do not have an alternative explanation. His explanation is, very roughly and in my emphasized-non-understanding, that the electromagnetic wave from the laser is continuous. It is smaller but non-zero and not discrete. His claim is that it works because of the laser light source, because the laser makes the light source coherent. He claims that, were the light source not coherent, interference would not be observed.

At this point, I refer to my chosen avatar image on this forum. The joke went over my head.

Can anybody wield the clue-bat and help me understand what is happening here? How do we get a quantized field that can interfere with itself 1.6 million wavelengths away? I would be pleased either with explanation posted here or pointers to things I should read on my own. If the latter I will make a serious attempt to report back with what I find.

 

[PeterDonis]

How do we get a quantized field that can interfere with itself 1.6 million wavelengths away?

It's not. The interference is occurring at particular points on the detector, where waves from both slits come together. The 1.6 million wavelengths is the difference in the path lengths that the waves from the two slits have to travel to come back together; but that doesn't mean they are interfering with each other when they are that far apart. Roughly speaking, it means you have to leave the laser on for a long enough time that waves can travel over both paths and come back together at a particular point on the detector and interfere with each other.

 

[PeterDonis]

His explanation is, very roughly and in my emphasized-non-understanding, that the electromagnetic wave from the laser is continuous.

This corresponds to my statement that you have to leave the laser on for a long enough time for waves to travel over both paths.

His claim is that it works because of the laser light source, because the laser makes the light source coherent. He claims that, were the light source not coherent, interference would not be observed.

This corresponds to the fact that the wavelength has to be consistent over a distance corresponding to the longest path--i.e., there can't be any significant variation in the wavelength over at least that distance. If there were significant variation in the wavelength over the longer distance, the wavelengths of the two waves coming back together at a particular point on the detector wouldn't match up closely enough to get sharp interference fringes; you would just see a muddle.

 

[WernerQH]

He still observes interference when both paths are open, but not when either is closed. The different path lengths are roughly 1.6 million wavelengths different.

This is quite well understood with classical optics -- coherence time (coherence length) is the crucial concept. You cannot have a discernible interference pattern without sufficient phase stability of the light source.

The propagation of light is well described with the (continuous) wave picture. But the interaction of light with matter (absorption and emission) is inherently discontinuous, as Einstein dared to suggest in 1905. Absorption and emission of light occurs in "lumps", and this nice experiment shows that we really need both the wave and quantum pictures. Incidentally, this same experiment has been discussed in a previous thread.

 

[vanhees71]

That's true, but indeed there are states of the electromagnetic field, which have no classical analogue. One example are single-photon states, and indeed there are phenomena, which clearly demonstrate the necessity for field quantization, like "quantum beats", spontaneous emission, or the "HOM experiment".

It's also clear that even single photons can neither be understood as classical particles since they are not even in principle localizable nor as classical em. fields. Fortunately today we have a consistent theory, describing all aspects of electromagnetic phenomena with high precision correctly, QED. For almost 100 years, there's no need for the old quantum theory with its inconsistencies like "wave-particle duality" anymore.

 

[WernerQH]

Fortunately today we have a consistent theory, describing all aspects of electromagnetic phenomena with high precision correctly, QED. For almost 100 years, there's no need for the old quantum theory with its inconsistencies like "wave-particle duality" anymore.

Yes, QED is a fantastistic success. But it doesn't make the puzzling combination of "particle" and "wave" features of light go away.

Can anybody wield the clue-bat and help me understand what is happening here? How do we get a quantized field that can interfere with itself 1.6 million wavelengths away?

The problem is the many misleading connotations of the words "wave" and "particle".
Light is neither. One should concentrate on the observed phenomena and refrain from assumptions about what "really" travels from the "source" to the "detector".

Richard Feynman tried to describe the essence of QED in his book "QED - The Strange Theory of Light and Matter". Perhaps it can ameliorate your puzzlement.

 

[vanhees71]

Yes, QED is a fantastistic success. But it doesn't make the puzzling combination of "particle" and "wave" features of light go away.

It does! There is a, admittedly pretty abstract mathematical description, of all phenomena including all the quantum effects, QED without assuming self-contradictory concepts like "wave-particle duality".

The problem is the many misleading connotations of the words "wave" and "particle".
Light is neither. One should concentrate on the observed phenomena and refrain from assumptions about what "really" travels from the "source" to the "detector".

Exactly, all you can observe (also accoring to QED) are detector responses to electromagnetic fields, and only these detector responses are localized by the position of the detector (like the pixels in a modern electronic detector).

Richard Feynman tried to describe the essence of QED in his book "QED - The Strange Theory of Light and Matter". Perhaps it can ameliorate your puzzlement.

 

[Grelbr42]

So, after some extra reading and thought, here is my understanding.

The laser produces a wave function that corresponds to a large number of photons, all in phase. That is, we have a $\Psi$ where the normalization is not 1, but some very large number. In this case, at least several millions. And this wave function extends over a distance along-the-path of at least some meters. Possibly much larger than a few meters.

Insert here the usual explanation of how a continuous output laser works. Mirrors at each end, energy being supplied to the lasing material, small aperture, passing photons stimulating emission of new photons in phase, round up the usual suspects.

When the wave function interacts with the interferometer, the shifted parts interfere either destructively or constructively. Thus the interference pattern.

So the issue is, as it has always been, the observation problem. How does a wave function that extends over some macroscopic distance manage to get observed at a specific location? It isn't a new problem here, but the same problem in a different costume.

Even the filters before the interferometer are the same issue. One might suppose that stripping out one photon from the uniform coherent wave function might produce a wave function with a hole. Or at least a step function of some kind. That is, you might expect that removing one photon might produce something generically like the following.

And if the wave function after the filters were "bumpy" in this fashion, how could an interference pattern develop? If photons are "digital" then how does the filtering process produce an output that is still both coherent and uniform in amplitude? The same way as previously described. Extracting one photon's worth of energy does not make a hole in the wave function. It decreases the normalization by one. The dip just shown is wrong. The filter removes one quantum of energy and correspondingly one quantum of amplitude from the entire wave function. It is the observation problem again, in still another costume.

 

[Nugatory]

How does a wave function that extends over some macroscopic distance manage to get observed at a specific location?

It isn't a wave function in the sense of the quantum mechanical wave function (which is a complex-valued function in an abstract mathematical space), it is an electromagnetic wave, oscillating electrical and magnetic fields obeying Maxwell's classical equations of electrodynamics. Measuring at a specific location is done by measuring the strength of the fields at that location.

One might suppose that stripping out one photon from the uniform coherent wave function might produce a wave function with a hole. Or at least a step function of some kind. That is, you might expect that removing one photon might produce something generically like the following.

That's not how photons work. Absorbing one photon in a beam of coherent and monochromatic light just leaves you with a (very slightly) less intense beam as tiny part of the energy and momentum of the beam is transferred to the absorber.

 

[vanhees71]

A photon is a specific state of the quantized electromagnetic field. It's a single-particle Fock state of (asymptotically) free fields.

A coherent state is a state with unspecified photon number, which is Poisson distributed in such a state. For high intensities it can be described by the classical electromagnetic field limit.

 

[Grelbr42]

It isn't a wave function in the sense of the quantum mechanical wave function (which is a complex-valued function in an abstract mathematical space), it is an electromagnetic wave, oscillating electrical and magnetic fields obeying Maxwell's classical equations of electrodynamics. Measuring at a specific location is done by measuring the strength of the fields at that location.

It is a wave function. That's why we get interference and why we see discrete events. We don't measure the strength of the fields at a location, we either see or don't see an indicator on a detector.

That's not how photons work. Absorbing one photon in a beam of coherent and monochromatic light just leaves you with a (very slightly) less intense beam as tiny part of the energy and momentum of the beam is transferred to the absorber.

I suppose it was too much to ask for you to read to the bottom of the paragraph where I said pretty much that.

 

[PeterDonis]

The laser produces a wave function that corresponds to a large number of photons, all in phase.

Not quite. It produces a coherent state, which has no definite photon number. The expectation value of photon number in the state can be as large or small as you like, depending on how the intensity of the laser is set. In your OP, you specified a very low intensity, corresponding to an expectation value of photon number of something like 1/250.

Whether you want to call a coherent state a "wave function" is a matter of terminology, not physics. Photons are generally not considered to have a "wave function" because they can't be localized (in more technical language, Newton-Wigner localization does not work for massless fields). The more general term "quantum state" would be a better choice.

As for how the interference is produced, see my posts #2 and #3.

 

[PeterDonis]

Extracting one photon's worth of energy does not make a hole in the wave function. It decreases the normalization by one.

This is not correct. An idealized coherent state is an eigenstate of the photon annihilation operator, which means it is left unchanged by the operation you are describing as "extracting one photon's worth of energy".

A real laser does not quite produce an idealized coherent state, so the state of a real laser's light will be changed somewhat by measuring a photon. But "decreases the normalization by one" is still not a correct description of the change.

 

[PeterDonis]

Absorbing one photon in a beam of coherent and monochromatic light just leaves you with a (very slightly) less intense beam as tiny part of the energy and momentum of the beam is transferred to the absorber.

One has to be careful here. The OP specified that the intensity of the laser is very low, corresponding to an expectation value of photon number of about 1/250. There is no way to interpret detecting one photon from such a beam as "taking one photon's worth of energy and momentum out of the beam".

 

[vanhees71]

Particularly for photons the 1st-quantization formulation, which is very successful in non-relativistic QT, is inapplicable. The reason is that photons are massless "particles" (I'd prefer to talk about quanta only, because the naive particle picture is utmost wrong for photons, but that's unfortunately the terminology used) and can be destroyed and created very easily. That's one of the many reasons why the only adequate description of photons (and also generally for relativistic QT) is (local) relativistic quantum field theory, which is perfectly suited to describe creation and annihilation processes.

It is also important to understand that a laser, even if dimmed down very much, does not produce single-photon states but rather socalled coherent states, which describe a situation, where the photon number is indetermined. The probability distribution for measuring a given number of photons is a Poisson distribution. For a coherent state describing very low-intensity laser light, the average photon number can be as low as you like (even <1). Then the most probabable finding is that there's no photon at all, and already the probability for finding a single photon is very small, but that's not a single-photon state but rather "mostly vacuum". For very large intensity the coherent state can be well approximated by the classical approximation, i.e., it can be understood as a classical em. wave field.