Undergrad Single Photon States: Definition & Real-Life Applications

[vanhees71]

But what are you making of the above constructed normalizable state which is an eigenstate of eigenvalue 1 of the photon-number operator? I don't think that it contradicts in any way the Reeh-Schlieder theorem, and of course it can't, because it's free-field theory, which is well-defined. I think the Reeh-Schlieder theorem simply doesn't apply here, because it's precisely not a state that describes a "localized photon". I think it's just the mathematical rigorous version of the old gedanken experiment by Rosen and Bohr about the impossibility to localize relativistic quanta: Trying to confine even massive particles you rather create new particle-antiparticle pairs than localizing the single particle to a small volume. That's the more true for photons, which as massless spin-1 quanta don't even admit a position observable.

Also what then do you think are the "single photons" used by Clauser in the above quoted historical experiment or the "heralded single photons" in modern preparations using parametric down conversion, all of which clearly show the "single-photon features" like antibunching in the HOM experiment, etc?

 

[LittleSchwinger]

I don't think that it contradicts in any way the Reeh-Schlieder theorem, and of course it can't, because it's free-field theory, which is well-defined. I think the Reeh-Schlieder theorem simply doesn't apply here, because it's precisely not a state that describes a "localized photon"

I agree.

That state is a perfectly valid Fock state, but no realistic preparation procedure in a finite volume can prepare it, i.e. it's an "idealization".

Just to be clear to others. Single photon states definitely exist mathematically as valid states, it's just that no preparation procedure in a finite volume can prepare them.

One can take the idealized limit where the preparation device is infinitely large and then these states can be prepared, but of course this isn't a real procedure. And of course in the actual de Sitter cosmology of real life this limit can't be taken, so we must also be using the idealization of Minkowski space.

I think it's just the mathematical rigorous version of the old gedanken experiment by Rosen and Bohr about the impossibility to localize relativistic quanta: Trying to confine even massive particles you rather create new particle-antiparticle pairs than localizing the single particle to a small volume. That's the more true for photons, which as massless spin-1 quanta don't even admit a position observable

Correct. And I just want to say, that Bohr-Rosen work is a phenomenal paper. I don't know if you've ever seen Freeman Dyson's thoughts on how it relates to gravity. Interesting food for thought.

Regardless yes, the Reeh-Schlieder theorem is nothing but a "rigorous" version of that work.

Also what then do you think are the "single photons" used by Clauser in the above quoted historical experiment or the "heralded single photons" in modern preparations using parametric down conversion, all of which clearly show the "single-photon features" like antibunching in the HOM experiment, etc?

States arbitrarily close to single photon states, so that they effectively are single photon states FAPP. My point is of course complete pedantry that would have me kicked out of an actual lab

 

[vanhees71]

This I fully agree with. For me the best heuristic introduction to relavistic QFT I've seen yet is in S. Coleman's Lectures:

S. Coleman, Lectures of Sidney Coleman on Quantum Field
Theory, World Scientific Publishing Co. Pte. Ltd., Hackensack
(2018), https://doi.org/10.1142/9371