Scully’s DCQE paper 1999 - reasons for phase shift

Question

http://Arxiv.org/abs/1103.0117

Or better Google the paper using string:
arxiv:quant-ph/9903047v1

In order to “see” (detect) the interference pattern 
we have to take care about the shift of Lambda between D0D1=R01 in Fig.3 and D0D2=R02 in Fig.4.  We can “see” (detect) interference only when we are able to distinguish “red slit A” and “blue slit B” photons.

My questions are:

Which causes contribute to the lambda shift?
Just the 50:50 splitter BSc or as well others like 
Glan-Thompson prism or even the PS prism?
If I would not erase the “which-way” information with current BSc Mb Ma D1 D2 and would remove these elements and if I would rotate additionally BSa and BSb so that the photons would path without being mirrored or detected and would travel a save distance further (10m? or more?) than the corresponding entangled photons have to travel to detector D0, ... would I get an interference pattern at D0? Would I get no Lambda shift between photons of path A slit (red) and path B slit (blue) ( I used classical physical words to be short)? Would I avoid any shift between the two independent pattern so that I would not need any additional information at D0 to detect interference?
Am I able to measure an interference at D0 detector without any information of the coincidence counter? In current arrangement of the experiment the lambda shift would cause the adding of the 2 interference pattern having a lambda shift so that the accumulated pattern would show no more an interference pattern depending on the amount of lambda! Without any information of the coincidence counter and the difference between D1 and D2 related entangled events I would see no interference at D0. 
Is there any eraser which would not cause a Lambda shift or any other cause so that interference could be seen?

PhysicsDave · Answer

1) Lamda shift is only caused by the the path differences (length, phase delay) in the 2 interference arms (idler) and these path differences are entangled with the path differences measured at D0 because the 2 photons shared a common wave function.

2) I think to cause interference you need idler paths or paths.

3) Yes there would be no interference, you need the coincidence counter to find the interference.

4) Because we need to monitor 2 slits we need 2 interference arms and there is always a lamba.

Michael W · Answer

If lambda would be a function of different length of signal path and idler path we might set it to zero by precisely measured distances.

But is it really a function of distance difference and frequency of used photons? Because Scully et al used linear polarised laser beam as quantum well laser. I guess lambda is related just to change of direction of Polarisation.

Many years ago John Archibald Wheeler had a Test with Quasar light passing a Galaxy left and Right side the Galaxy and as the Galaxy works like a Lens the light crossed at our earth and we can see the interference. So he got no lambda shift at all. This can be the evidence for being independent of different path length and wave length of light.

fishinear · Answer

The BBO crystal imposes a random phase difference between the two paths of the photon. That is the reason you don't see an interference pattern at D0 if you take all photons together. The wave function for each photon individually shows an interference pattern at D0. But they all have a different phase difference between the paths, and therefore the individual patterns are all shifted differently, and add up to a single bulge at D0.

It is the BBO crystal that causes the phase difference. The BSc mirror kind of acts like a filter for the phase difference. It sends photons with certain phase differences to D1, and with opposite phase differences to D2
Nothing that you change at the D1-D4 side influences the pattern at D0. You always get the single bulge pattern there.
It should in theory be possible to install a half silvered mirror similar to the BSc/D1/D2 setup on the D0 side as well. The mirror would filter half of the photons based on phase difference, resulting in a net interference pattern. If you would then use a coincidence counter to compare the result with the B3/B4 photons, then it should show an interference pattern slightly shifted one side or the other. That is, you should see an intersection of the "which slit" pattern, and the "both slits" pattern.

Scully’s DCQE paper 1999 - reasons for phase shift

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