vanesch said:
What happens, is simply this: when you put the perpendicular polarizers in front of each slit at B, you DO NOT GET AN INTERFERENCE PATTERN.
This is true because orthogonal waves cannot interfere. There is confusion because polarized light shone upon both slits will still behave normally, and that is what is meant when one reads that polarizing photons will not affect them in double slit experiments. Polarizing one slit differently from the other is a different matter and does affect interference, making it impossible.
vanesch said:
However, when you now put a polarizer at 45 degrees in front of detector A, and you PICK THE COINCIDENCES of A and B (this removes about half of the photons at B, which do not correspond to a click in A), then it turns out that this SUBSAMPLE shows an interference pattern.
This is where much of the confusing originates. The filter at A only polarizes about 50% of both x and y-axis A photons to diagonal. Or, you could say, it is passes 50% both x and y polarized photons (which are always being passed anyway if there is no filter), now they will all be diagonal. However, the photons at B get polarized too, to diagonal. There is no ignoring of half the hits at B ("this removes about half of the photons at B, which do not correspond to a click in A"). Since 50% of the photons at B get polarized to diagonal too, they pass through the quarter-wave plates without making the right-hand and left-hand tell-tail photons, but instead the photons leaving each side are the same, which naturally causes an interference pattern. All of the photons at B detector still coincide with their matching partners at A. There are no non-corresponding hits at B (except for noise photons which are always ignored no matter what).
vanesch said:
But given that you don't know the polarization of the pair (given that your A-click was after a polarizer at 45 degrees), you will not be able to say through which slit its partner went.
This is true because the idler photos at A are being polarized the same. An x photon now is diagonal, and a y is now diagonal. As mentioned above, only about 50% of horizontal or vertical photons make it through a diagonal filter, but those that do still emerge diagonal, so their associated entangled photons will be diagonal too, and only those will be counted by the coincidence counter.
vanesch said:
However, if you put the A polarizer to 90 degrees, or to 0 degrees, AND ASK COINCIDENCE AGAIN, you will have a subsample at B that will NOT show interference. This is because knowing the click at A, you know what polarization its partner had, and hence through which slit it went at B.
This seems to be giving the impression that both possibilities are always at detector B, and we just see one or the other by filtering out half of the information at B by turning the polarizer at A. In actuality (as already mentioned), the A polarizer not only polarizes the A photons to diagonal, but also the B photons to diagonal because they are entangled. Turning the A polarizer to 90 degrees or to zero degrees also does the same to the entangled photons at B, and this causes the polarizations at B to be orthogonal again, disallowing interference.
vanesch said:
But in no case, by doing something at A, you see something change at B WHEN ONLY LOOKING AT B.
There is no screen at B, only a detector that moves back and forth picking up fringe patterns in that manner. Only some of the photons that enter the BBO crystal are entangled, the rest are considered to be noise. So, what affect that may have on a visual image could be taken into consideration. Any light going through the double slits should produce a fringe pattern, whether entangled photons or the noise photons. Once the quarter-wave plate filters are installed, the interference pattern should go away as long as the incident light is either horizontal or vertical polarization, as both the entangled pairs and the noise photons are (Keep in mind that the diode laser pump that produces all the photons linearly polarizes all of them). But, when a diagonal filter is placed at A, only entangled pairs at B will be polarized, so visually fringes may not arise again, since any horizontal and vertical noise photons will still result in a bar pattern. It's difficult to say what it would look like, perhaps both patterns would appear at once.