I Does Relativistic Motion Impact Quantum Optical Experiments?

[Swamp Thing]

If we are considering a problem involving generic photon emitters and detectors that are moving at various relativistic velocities with respect to each other, do we need to move outside of non-relativistic quantum optics?

I'd like to stress that this question is not about any definite species or flavor of massive particles moving at relativistic velocities. (That would, IIUC, take us into QFT). But I'm asking here about generic photon emission events and photon detection events where the rest frames of the emitters and detectors are different. The detectors interact only with propagating free photons, and no massive entities interact directly with each other.

 

[John Morrell]

Could you specify more about the problem? Obviously if what you're measuring has a lot to do with the time things occur it will have a big impact, but there are a lot of other ways it could change things, it just depends on what you're looking for.

 

[Swamp Thing]

For example, take a Hong-Ou-Mandel experiment. In the usual version, of course the emitter and the detectors are all in the same rest frame, and the source emits photons at the same wavelength.

But let's consider two entangled photons emitted at different wavelengths. (I believe this happens in SPD if the alignment is chosen in a certain way). In the rest frame of the emitter and apparatus, the detectors will receive photons at different wavelengths, so the usual interference will not occur. But if the one detector is moving towards the beam splitter and the other is moving away from it, then the Doppler shifted wavelengths will match. And as it happens, the path lengths after leaving the splitter don't have to be equal anyway. So, would we see the HOM effect, at least in principle? (Of course, I understand that it is difficult enough, in practice, to make it work in a lab --- so it would be that much harder with moving apparatus).

But to get back to my question -- in principle, can we analyze this correctly, merely by applying the correct Doppler shifts and then following the usual quantum optics route?