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When a single photon enters a non-polarizing beam splitter, in any of the two inputs, it has 50% chance of leaving by each of the two outputs.

When two photons enter this beam splitter, each by one input, they will always leave it together if they have the same polarization (and if they entered it synchronized). There will be 50% chance they will leave by one output and 50% chance they will leave by the other, but they will leave together.

When the two photons don't have the same polarization, a combination of chances of leaving together and alone, by each output, happens depending on how synchronized they were and what was their initial polarizations.

My question is what happens when you have two photons leaving the beam splitter together, and then they enter another beam splitter with a third photon.

Will they leave it together if the three have the same polarization as happens with only two? And what about when the photons don't have the same polarization?

What is the generalized description of a beam splitter to any number of photons entering any of the inputs, with any polarization?

Thanks.

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  • $\begingroup$ What have you tried? $\endgroup$
    – Norbert Schuch
    Commented Apr 17, 2022 at 23:05
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    $\begingroup$ I have the output wavefunction of the first beam splitter. I use creation and destruction operators to get it, but I know only how to get the relation between these operators to the case of two photons entering the splitter, not three, then I can't find the wavefunction after the second beam splitter. $\endgroup$
    – Vinicius Araujo Ritzmann
    Commented Apr 17, 2022 at 23:22
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    $\begingroup$ found this, it might be relevant copilot.caltech.edu/documents/16791/… $\endgroup$
    – anna v
    Commented Apr 18, 2022 at 4:31
  • $\begingroup$ Yeah thanks that really helped. It adresses many scenarios, some I didn't think about yet and helped me finish the problem I had. $\endgroup$
    – Vinicius Araujo Ritzmann
    Commented Apr 18, 2022 at 11:21

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