Signal photon patterns in the Delayed-Choice Quantum Eraser experiment of Kim et al

Question

Full explanation of the experiment in the Wikipedia page for the delayed-choice quantum eraser.

The experiment of Kim et al. (Phys. Rev. Lett 84, 1 (2000), arXiv:quant-ph/9903047):

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Distribution of signal photons at $D_0$:

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(signal photons are the ones going through the yellow lens and idler photons are the ones going down)

The wikipedia page states "The total pattern of signal photons at the primary detector never shows interference" (primary detector is $D_0$)

We must sort the signal photons into four streams that reflect the states of the idler photons at their four distinct detection screens in order to isolate the interference pattern or no-interference pattern. ($R_{01}$, $R_{02}$, $R_{03}$ and $R_{04}$ are simulated distinct detection screens)

Would the isolated patterns $R_{01} + R_{02}$ equal $R_{03} + R_{04}$?

Answer 1

In a word, yes. The interference fringes in $R_{01}$ and $R_{02}$ are offset by half a fringe spacing, in such a way that if you add the two, the fringes get completely erased, and the pattern matches exactly what you get if you add together the two complementary non-interfering patterns.

Pulling the plots from this later answer, this is what a realistic set of distributions looks like for the Wikipedia standard setup:

Both $R_{01}+R_{02}$ and $R_{03}+R_{04}$ add up to $D_0$.