Question about the interference effect with two distinct sources.

[al onestone]

The optical two-source interference effect due to Hull (1949) has largely been overlooked by the history of quantum mechanics. Mandel and Fleegor brushed up the effect by reducing the signal strength of the sources and reducing exposure times for interference collection. In the end this effect was only looked at for its theoretical insights concerning the photon/EM wave. But is there more to this effect? Can it be used for other purposes like spin/polarization recombination of photons?

The question is about the use of two-sources for optical effects other than simple indistinguishability interference. Is it possible to produce a coherent state by combining (with a beamsplitter) two sources which have distinguishable states, let's say one horizontally polarized (H) and one vertically polarized (V)? Obviously you cannot get interference from such a combination but one might still get a small portion of the output which is in a coherent state, H + V. Only the portion of the two beams that are "in phase" would project onto a coherent state of 45degree polarization, much like in the conventional two-source interference effects where the "in phase" portion is postselected with an appropriate method. Of course the method of postselection would have to be different but it is possible to filter out the coherent portion of the output if there is a coherent portion. I'm wondering if anyone in the literature has actually tried this type of thing before, or if there is some form of evidence as to why it would not be possible, experimental or theoretical.

The basic thought experiment I'm proposing is shown in the attached figure. In this setup only the 45deg polarized portion in a coherent state would produce a double slit interference pattern. It suffices to say that there are other methods to produce an effect if indeed there is a coherent projection onto the 45deg state (H + V) at the beamsplitter.

 

[Simon Bridge]

Looking for the question, found:

Is it possible to produce a coherent state by combining (with a beamsplitter) two sources which have distinguishable states, let's say one horizontally polarized (H) and one vertically polarized (V)?

Do I understand you? You want to know it makes sense to describe and experiment using two sources with distinct states using a superposition of their state-vectors?

 

[al onestone]

I want to know what happens when you add two distinguishable states (like H and V) from separate sources. If you add them at a beamsplitter we would expect to have an incoherent mixture described as,

ψ = lH>*lI> + lI>*lV> where I is the identity

However if a small portion of the two beams are in phase (just like in the two source interference effect) then you would expect this portion to project onto a state of mixed polarization as,

ψ = lH>*lI>*lI> + lI>*lV>*lI> + lI>*lI>*lH+V>

which has a third component of the state vector for the coherent portion.
My question is "Is there validity to the idea that there is a projection at the beamsplitter onto a state of coherent mixed polarization, for the portion of the combined beams that was in phase?"