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I have a train of pulses (with some known time separation between them) and I want to mix two of these (perform an XOR - beam splitter transformation - between them), leaving the rest alone. How do I do this?

If the pulses were separated into different spatial modes I could just take a regular beam splitter and stick the two modes I wanted into it, but how can this be done in time?

Equivalently is there a way to efficiently change the basis of an optical pulse train to the spatial domain?

We can assume the pulses are identical up to a binary phase (which is wy the BS transform will give an XOR).

A restriction is that I won't know very long in advance which modes I want to mix, and it will be given differently each run of the experiment.

It seems like there should be an off-the-shelf thing that does this (some kind of commercial (de)multiplexing device)?

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This is generally doable if you are able to switch the photons into different modes (i.e. you have optical switches that are faster than the separation between your pulses). You can then put the first photon into a line delay (essentially a loop of fibre optic) and you will have your two photons running synchronously on spatially separated modes. You can then do your XOR/PBS/whatever operation you need to do.

To see an example in action, try

Active Temporal Multiplexing of Photons. GJ Mendoza et al. arXiv:1503.01215.

I have no idea if there are commercial multiplexers available that will do this and match your needs, though. If the pulse separations are long enough you will hopefully be able to find a general multiplexer that you can then fit out with spools of fibre. If your specs are demanding then I suspect you'll be forced, like the Bristol group, to build much of it in house.

Good luck, and happy experimenting!

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