Kim et al DCQE optical details

[Derek P]

I am (still) trying to understand the optics of the Kim et al DCQE set-up. It is the optics of the "erased" cases that I don't understand.

These are the entangled pairs where the "idler" photon is detected by D1 and D2. Each detector receives a contribution, from one slit, that has passed through the beam splitter and another, from the other slit, that has been reflected from it. The diagram looks pretty symmetrical. Yet there is actually a +/- 90 degree phase offset for the two contributions. This causes the two patterns (created by the correlator) to be offset by 180 degrees so their peaks and troughs cancel. Indeed they must cancel because the raw pattern at D0 itself is not an interference pattern.

Please note I'm not asking about the nature of the two-photon state. I just don't know where that wretched (but essential) 90 degrees comes from!

Thanks

 

[Dadface]

The diagram is not symmetrical. Look again at the rays reflected from Bsc. One of them is reflected upon meeting a more dense medium and undergoes a phase change of 180⁰.

 

[Derek P]

The diagram is not symmetrical. Look again at the rays reflected from Bsc. One of them is reflected upon meeting a more dense medium and undergoes a phase change of 180⁰.

Of course. But that applies to both detectors. D1 receives a reflected blue ray and a transmitted red. D2 receives a reflected red ray and a transmitted blue.

So, yes, as they emerge from the beam splitter the two "ray-superpositions" should be 180 degrees out of phase with each other. However. that is of no interest because they are about to be detected and phase is irrelevant. You could get the same effect by moving one of the detectors by half a wavelength! The phase that matters is the phase difference between the red and blue components within each superposition since it is this that determines the detection rates at D1 AND D2 and therefore the allocation of the signal photons to their respective patterns.

 

[Dadface]

I don't quite understand your comment but the two patterns are out of phase due to one of the reflected rays undergoing a phase change of 180⁰. This is because that ray is reflected from a more dense medium The other reflected ray is reflected from a less dense medium and does not undergo a phase change.

 

[Derek P]

I don't quite understand your comment but the two patterns are out of phase due to one of the reflected rays undergoing a phase change of 180⁰. This is because that ray is reflected from a more dense medium The other reflected ray is reflected from a less dense medium and does not undergo a phase change.

Oh! Got it! Thanks! You didn't understand my comment because I had completely missed the point. Sorry!

I'd been staring at that picture for a year and never noticed that the reflection in the beam splitter is shown on just one "face". I was thinking in terms of a half-silvered mirror, not, as implied, reflection at a change of medium.

Thanks again.