How do photons interfere with each other/themselves?

[xtempore]

When looking at information about the double-slit experiment, you often see statements like...
"the photon interferes with itself".

But what does this actually really mean?

In the classical analog of waves it's easy to understand that troughs and peaks can cancel each other out. But can a photon cancel itself or another photon?

Assuming that N photons pass through the slits, do N photons still strike the screen?

If so, then isn't this essentially just a different type of diffraction?

And if not, where the heck do they go?

 

[peter0302]

When looking at information about the double-slit experiment, you often see statements like...
"the photon interferes with itself".

But what does this actually really mean?

The possible _paths_ the photon can travel interfere with each other like a wave.

In the classical analog of waves it's easy to understand that troughs and peaks can cancel each other out. But can a photon cancel itself or another photon?

Two photons can certainly destructively interfere with one another if they are 180 degrees out of phase. An "anti-laser" so to speak.

Assuming that N photons pass through the slits, do N photons still strike the screen?

Of course.

If so, then isn't this essentially just a different type of diffraction?

No, because if it were simple diffraction, you'd just see two blobs merge into one big blob. Instead, you see an interference pattern that you cannot generate from any classical particle-like explanation.

And if not, where the heck do they go?

They hit the screen, just not at the interference minima. They hit somewhere else - they tend toward the maxima.

 

[xtempore]

Thanks. I think that mostly answers my question.

So essentially the whole analog of using water waves is really a very poor example. The minima there are due to a peak and a trough canceling each other out.

Whereas with a photon (if I understand correctly) the wave function interferes with itself in such a way that the photon has a 0% chance of striking a minima, and the probabilities increase towards each of the maxima.

Since writing this question I also stumbled across the information that the interference pattern is almost entirely the result of single photon interference, and that interference between two or more photons is extremely rare and would result in a different pattern.

This whole quantum probability thing still bugs me. I can't seem to get past my mental block that tells me that the physical world is deterministic. I just feel like we're missing something.

 

[peter0302]

That's right. Well, I think the water waves analogy is perfectly fine, as long as you don't confuse the water waves with the photons themselves. The wave FUNCTION is what behaves like a water wave. The photon is still a particle. The interpretation of the physical meaning of the wavefunction is a subject much debated here and elsewhere.

That's also right that two-photon interference is not the same as one-photon interference. Again, what is interfering in the double slit is the branches of the wavefunction representing the two paths the photon can take - there's still one photon, etc. One reason we know this is that electrons behave exactly the same way - and no one ever thought they were waves before that.

 

[Count Iblis]

Two photons can certainly destructively interfere with one another if they are 180 degrees out of phase. An "anti-laser" so to speak.

This is not true. Suppose you have two identical lasers and do an interference experiment (I think in practice two different lasers can only stay coherent for a very short time, but it is possible to do intereference experiments). Then how does that interference pattern arrise? It is not due to any interaction between the photons from the two lasers at all!

Instead, what happens is that both lasers contribute to the creation of individual photons and you cannot tell which laser created any individual photon. So, it is exactly analogous to the two-slit experiment in which you cannot tell from which slit any photon that hits the screen comes from.

The interference pattern in the two lasers experiment would also exist if the power of the lasers were turned down so that the interference patern would be build up very slowly photon by photon (but in practice one probably cannot arrange for the two lasers to remain coherent for a long enough time to do such an experiment).

 

[peter0302]

I did not say that interference in a two-slit experiment was due to two photon interference. The OP asked if two-photon interference was possible at all, and of course the answer is yes.

 

[Count Iblis]

I did not say that interference in a two-slit experiment was due to two photon interference. The OP asked if two-photon interference was possible at all, and of course the answer is yes.

You cannot get two photon interference in the way you described. Also, in the literature "two photon interference" is used to denote interference of two photon states, in which the same two photon state can evolve via different paths and you don't have the "which path information". So, that's again exactly analogous to the case of single photon interference.

You cannot have interference due to different photons somehow "canceling each other out". In the (perhaps hypothetical) case of two lasers, the inteference pattern doesn't arise in that way at all I as I explained above.

 

[peter0302]

That is exactly how holograms are created. A laser is sent to a beam splitter. One half of the beam illuminates the object which scatters the light onto photographic film, while the other half is shone directly on the film. The convergence of the two beams results in an interference pattern on the film which, when laser light is subsequently shone on the developed film, creates the 3D image. This is not "one photon interference" as in a quantum experiment. It is two sets of photons (millions and millions from each half of the beam) converging and interfering according to their phase alignment, as determined by the object being holographed.

Could you create a hologram one photon at a time? The object being holographed is not a mirror usually, and so the photons scattered from the object ought to be distinguishable from the photons coming directly from the laser - and we all know that if the photons are distinguishable, no quantum interference pattern is generated.

 

[Cthugha]

Could you create a hologram one photon at a time?

Yes, you could, although it depends on what you mean exactly with one photon at a time. Coherent light with any average intensity will produce holograms. However, most of these thought experiments concerning "one photon at a time" are flawed because a coherent state with low average intensity is not the same as a n=1 Fock state, which is closer to the common understanding of "one photon at a time".

The object being holographed is not a mirror usually, and so the photons scattered from the object ought to be distinguishable from the photons coming directly from the laser - and we all know that if the photons are distinguishable, no quantum interference pattern is generated.

Why should they be distinguishable? Not every kind of scattering breaks coherence. And - just as you said - if the photons were distinguishable, you would notice no interference pattern at all. Holography uses usual "one photon interference", although I think, that this term is very misleading as the underlying fields are the fundamental cause for interference to occur.

 

[peter0302]

The bottom line is that if you shine two photons 180 degrees out of phase with one another at the same point on a piece of film, the film will not be exposed. And that's exactly what's happening when you create a hologram.

It's possible if conditions were right that you could make a "quantum" hologram using a delayed choice Wheeler type experiment. But you don't need QM to make a hologram. You can treat the photons as though destructively interfering like two classical waves.

Perhaps we're saying the same thing.

 

[Cthugha]

The bottom line is that if you shine two photons 180 degrees out of phase with one another at the same point on a piece of film, the film will not be exposed. And that's exactly what's happening when you create a hologram.

Let me say it differently: The problem I have with this statement is, that in interference experiments photons are not the fundamental quantities - the underlying fields are.Considering this, it is difficult to speak of shining single photons with a certain phase in interference experiments. The underlying fields have a certain uncertainty, which is distributed among amplitude and phase. In a coherent state the uncertainty is divided evenly among both. So a coherent state does not have a clearly defined number of photons. You can never be sure, that you have just a single photon.

On the other hand have a look at single photons. This is a n=1 Fock state, where the amplitude is well defined, but the phase is completely uncertain. This incoherent light is certainly not suitable for usual interference experiments.

So you do not shine two photons with a phase shift of Pi somewhere, but you prepare two fields such, that you expect an average of one photon per given time interval and an expected phase shift of Pi, which is a small, but important difference.

 

[jtbell]

That is exactly how holograms are created. A laser is sent to a beam splitter. One half of the beam illuminates the object which scatters the light onto photographic film, while the other half is shone directly on the film. The convergence of the two beams results in an interference pattern on the film which, when laser light is subsequently shone on the developed film, creates the 3D image. This is not "one photon interference" as in a quantum experiment. It is two sets of photons (millions and millions from each half of the beam) converging and interfering according to their phase alignment, as determined by the object being holographed.

No, this is a single set of photons from a single source. Reduce the intensity of the source sufficiently, and you get one photon at a time going through the apparatus and arriving at the film. If there is no information available that can determine which way each photon goes, you get interference at the film.

If you try to use two separate lasers to produce a hologram, it generally won't work. In order to get it to work with two lasers, you have to make them so coherent with respect to each other that they behave effectively as a single source. To put it another way, in order for it to work, you cannot be able to tell which laser each photon came from!

 

[lcdisplay]

They are both saying the same thing, he noted that it was very hard to have to lasers be coherent but they can be via common seeding