Generally, in coupler when light goes through one input port of Y coupler it divides into two output. But my doubt is that , will they produce entangled photons as well in the output.
No it will not produce entangled photons. It will provide two possible paths for a photon, like Young's double slit experiment, and it the paths are recombined the result will show interference depending on the phase length of the two paths.
If a single photon were incident on an ideal 50/50 Y coupler, the output would be 1/sqrt(2)*[|0>|1> +|1>|0>] where the first ket indicates the number of photons in the upper branch and the second ket represents the lower branch. This is a spatially entangled Bell state.
Michael Belsley Malcolm White Thank you for your response Sir. I have another doubt. Kindly help.
If two identical photons in same polarisation state enters a 2X2 optical fibre coupler, in practice, what will be the probability of the photons to cross each others path.
Dear Mrigendra
I am not sure I understand your question, but here is an attempt at an answer.
In principal, an ideal 2x2 fiber coupler works just like a perfect free-space 50/50 beam splitter. If two identical photons enter the beam splitter with each input port receiving one photon, you have the same set-up as in a Hong-Ou-Mandel interferometer. The two photons will exit in the same output port, but which port they appear in will be random. In practice, the two photons have to arrive at the coupler at the same time (or at least within the photon's coherence time) which gives rise to the famous dip in the HOM experiment.
I think Michael Belsley 's two answers are right. However, I think you are thinking of photons in the wrong way. Photons are spread out. They can not only cross, they can be in the same place as each other. There are a few ways that they can interact with each other, but usually they don't. Each one has the same wave pattern as the EM wave solution for the beam they are in, but each can only be detected in one place, and that is where you see it. That place is determined by where the detector is, and where the photon can be. The interference pattern applies to every photon, and means that there are some places that the photon can't be found even if there is a detector there. In other places, the photon can be detected if you put a detector there, but if there are several detectors in different places where it could be found it will only be found by one of them. In most microwave and optics work the detector is smaller than the spread of the photon, so the size you measure for a photon detection is determined by the detector, not the size of the photon. The uncertainty principle applies to the detection, as well. In microwaves, for instance, if I use a lens to detect a wide photon, then a detector at the focus only detects a photon if it is from a small range of directions, so the uncertainty in position (lens width) is coupled with a reduction in uncertainty in the momentum in the direction across the lens (which corresponds to the angle of arrival). A detector consisting of a lens with small detector at its focus is an example of a large photon detector that may be larger than the photon. You can't tell where in the lens the photon arrived, but you can tell quite well what direction it came from.
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