Young's slits with incandescent light source

[TheHutch]

TL;DR

All modern versions of the double slit experiment use lasers to produce a coherent light source, but the experiment also works with sunlight (as originally performed by Young). This light is made 'spatially coherent' by passing through a single slit, but the transmitted photons will still have random phase relationships. How does interference arise with random phase photons?

I have been looking at various sources, especially the (now closed) thread on PF classical optics "Coherence, Young's double slit experiments."
The trick to making the double slit experiment work with incandescent, as opposed to laser, light is to pass it through an initial single slit 'to make it coherent'. Confusingly, this does not seem to be at all the same coherence as coherent laser light.
@sophiecentaur explained the resulting interference as follows:
"real light [...] can be thought of as consisting of many short wave trains. Each wave train will interfere 'with itself' when it is split between the two slits and meets on the other side."
As far as I can see, real light (from an incandescent source) consists of a stream of uncorrelated photons, with entirely random phase relationships, so these short wave trains can only be the individual photons, and the only way interference patterns can emerge is if these photons interfere only with themselves, and not with each other. The purpose of the single slit is simply to constrain the spatial origin of photons making the interference pattern crisper. In other words, the interference is a quantum phenomenon of individual photons, and not some aggregate wave nature of light. The fact that interference is still seen when reducing the photon flux down to one at a time should be no surprise at all.
Is that understanding correct? I haven't seen it in any text books (maybe I just haven't read enough).
For laser light, perhaps the photons' coherence make cross-photon interference possible (by making photons indistinguishable?), a bit more like the traditional wave explanation given in school text books. That makes the experiments simpler to perform, but obscures what is really going on.

 

[anuttarasammyak]

Photons do not interfere. Coherence of light does not matter. Interference takes place in a single individual photon. In loose saying a photon interferes with itself.

FYI experiment video of single photon Young double slit experiment by Hamamatsu Photonics in 1982. https://photonterrace.net/en/photon/duality/

 

[Cthugha]

Photons do not interfere. Coherence of light does not matter. Interference takes place in a single individual photon. In loose saying a photon interferes with itself.

FYI experiment video of single photon Young double slit experiment by Hamamatsu Photonics in 1982. https://photonterrace.net/en/photon/duality/

That is incorrect. Also, the experiment shown is not the double slit with single photons, but a double slit experiment done with a light field of an intensity of less than one photon on average. This is a huge difference.

Nobel prize winner Roy Glauber phrased this nicely (see this text on the ArXiv ):

" When you read the first chapter of Dirac’s famous textbook in quantum mechanics [8],
however, you are confronted with a very clear statement that rings in everyone’s memory.
Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,

'Every photon then interferes only with itself. Interference between two different photons never occurs.'

Now that simple statement, which has been treated as scripture, is absolute nonsense.
First of all, the things that interfere are not the photons themselves, they are the prob-
ability amplitudes associated with different possible histories. You can obviously have
different histories that involve more than one photon at a time. "

The coherence you see in a double slit is classical first-order spatial coherence. This is a fully classical measure. It is similar to the classical first-order temporal coherence you see in a Michelson interferometer. Temporal coherence tells you how monochromatic a light source is. If you have different frequencies within your light field, these will necessarily go out of phase over time, which reduces the ability to observe interference and defines first-order temporal coherence. If you have a spatially extended light source, the phases of the light fields emitted from different points will run out of phase after some distance, which reduces the ability to observe interference and defines first-order spatial coherence.
Obviously, you can make any light source more coherent by filtering it - put a spectral filter in to increase temporal coherence. Put a narrow pinhole in to increase spatial coherence.
Loosely speaking, first order coherence is a measure of how well we can predict the amplitude and phase of a light field, if we know it at a single position. First-order coherence is completely classical and has absolutely nothing to do with photons. It is not sensitive at all to the existence of photons - as one can see in the expressions in Glauber's notes they only depend on fields and not on occupation numbers. This indeed also means that it is no surprise that first -order coherence persists even for feeble light levels.

The coherence that defines a laser is instead second-order coherence. It tells you how well you can predict the intensity or (or photon number) of a light field at some time and position if you know its intensity here and now by detecting one photon. This actually tells you something about single photons - if you have a single photon here and now and detect it, the photon number in the future will simply be zero because the photon is gone. This is the physical signature of a single photon: It is not about the mean occupation number being below one, but about the impossibility to have two simultaneous detection events.

Laser light has the remarkable quality that detecting a photon does not change the relative probability to detect another one in the future at all, which makes coherent light extremely robust to external perturbations and losses. If you have incandescent light, the detection of a photon instead increases the probability to detect more of them. This sounds odd, but it is not at odds with conservation of energy. Rather, think of photons being emitted in large bunches of many photons for a short duration followed by almost no emission for another short duration and so on. Detecting one photon then just means that you are within one of these bunches and are likely to find more photons within this bunch. Accordingly, this effect is also called photon bunching.

 

[anuttarasammyak]

Thanks @Cthugha from your comment would it be correct to say that, in a single-photon double-slit experiment, the probability amplitudes associated with the photon's two possible paths interfere?

 

[Cthugha]

Yes, absolutely!

 

[sophiecentaur]

so these short wave trains can only be the individual photons, and the only way interference patterns can emerge is if these photons interfere only with themselves, and not with each other

I think this approach is, at best, confusing. Getting involved with photons to describe the mechanism of interference (and diffraction) just takes you down a rabbit hole. Conventionally, the actual form of a diffraction pattern involves integrating over the whole bandwidth of the beam of light. You have an aperture (or any objet in fact) and you look at the contributions (vector-wise) of all wavelengths involved and all possible transmission paths. That will tell you the sum of the waves passing through in any direction. Hence you will get a set of 'ideal' Young's slit patterns which will lay on top of each other and display an imperfect Young's pattern as the result of all combinations of wavelength and real (not ideal) path.

Once you have dealt with the problem using the above approach it may be 'interesting' to try it with photons- though I'm not sure how you could even visualise trillions of photons with different energies passing through the real slits. Where and when they are going to affect each other will depend on probability functions. Afaiaa, the final maths will have the identical form that the conventional Fraunhofer calculation gives you. Comparing and contrasting the two approaches if more a matter of philosophy; which method is 'right'?

 

[PeterDonis]

@TheHutch you seem to be trying to model all possible states of light in terms of "photons". Unfortunately, that's not a workable approach.

The fundamental object, so to speak, where light is concerned is the quantum electromagnetic field. The term "photon" is much more restricted; it refers either to a certain set of possible states of the quantum electromagnetic field (which are called "Fock states" and are very hard to produce), or to the fact that, if we make light faint enough, we always detect it as individual particle impacts (for example, if you run a double slit experiment with a very low intensity source, you will see individual dots on the detector screen that gradually build up an interference pattern).

An incandescent light source doesn't fit into either of those cases. It doesn't produce Fock states or anything remotely close to them, and you can't turn its intensity down anywhere near enough to see individual dots on the detector screen, you just see the interference pattern. So there's not going to be any good way to model a double slit experiment with an incandescent light source using photons.

Even in the low intensity case of a double slit experiment, with a suitable light source, there are issues with trying to model things using photons, which have already been described in this thread.