Question about Interference Patterns in Kim Delayed Choice Eraser

[msumm21]

I've looked at the DCQE paper by Kim, et al (arXiv:quant-ph/9903047) but I was not able to follow the math leading to the calculation of the patterns R_01, R_02, R_03, and R_04. Specifically, I was hoping to understand the source of the pi phase shift between R_01 and R_02. Is there a property of the idler photon (polarization, ...) that's different when it enters detector 1 as opposed to detector 2? Is there an "intuitive" explanation of how this relates to a phase shift in the signal photon pattern? Also, does anyone happen to know of a reference that explains the math of this to a reader like me that is not familiar with what these E+, A(*,*), ... functions are? Thanks!

 

[San K]

I've looked at the DCQE paper by Kim, et al (arXiv:quant-ph/9903047) but I was not able to follow the math leading to the calculation of the patterns R_01, R_02, R_03, and R_04. Specifically, I was hoping to understand the source of the pi phase shift between R_01 and R_02. Is there a property of the idler photon (polarization, ...) that's different when it enters detector 1 as opposed to detector 2? Is there an "intuitive" explanation of how this relates to a phase shift in the signal photon pattern? Also, does anyone happen to know of a reference that explains the math of this to a reader like me that is not familiar with what these E+, A(*,*), ... functions are? Thanks!

good question msumm21. Below is my guess (I am not a scientist/physicist)

See figure 2 of Kim paper:

- Beam splitter BS (in figure 2) creates a path difference- reflection Vs transmission

Also deviation angle (of the idler photon on emerging) from the Glan-Thomson prism - will create a phase differences however this would not explain the constant phase difference as it would be random I guess

 

[msumm21]

Hi San K. I may not completely understand what you are saying about the BS, so let me just say a few things here and maybe you can chime in with further comments. Everything below is referring to the idler photon unless stated otherwise. I think there are 2 paths to each of D1 and D2 as follows.

D1 paths:
prism -> BSA (transmit) -> MA -> BS (reflect) -> D1 (I'll name this path D1.1)
prism -> BSB (transmit) -> MB -> BS (transmit) -> D1 (name = D1.2)
D2 paths:
prism -> BSB (transmit) -> MB -> BS (reflect) -> D2 (name = D2.1)
prism -> BSA (transmit) -> MA -> BS (transmit) -> D2 (name = D2.2)

In both cases (D1 and D2) there is one path consisteing of 1 BS transmission + 1 BS reflection (paths D*.1) and another path with 2 BS transmissions (paths D*.2). Hence, I wouldn't think there's a difference caused by a different number of transmissions/reflections between D1 and D2 paths.

Are you referring to interference between the paths D1.1 and D1.2 (and also interference between D2.1 and D2.2)? Evidentially in half the cases D1.1 and D1.2 interfere destructively after BS and those cases correspond to 1 interference pattern from the signal photon, and then in another half of the cases D2.1 interferes destructively with D2.2 and those result in the PI-shifted interference pattern from the signal photon. However, I don't understand physically what the difference is in these two cases. Somehow a different polarization causes one of the other to have destructive interference and shifts the interference pattern of the signal photon? Something else?

Regarding the effect of the prism, I agree I wouldn't expect it to cause the PI phase difference.

 

[Cthugha]

In both cases (D1 and D2) there is one path consisteing of 1 BS transmission + 1 BS reflection (paths D*.1) and another path with 2 BS transmissions (paths D*.2). Hence, I wouldn't think there's a difference caused by a different number of transmissions/reflections between D1 and D2 paths.

Signs matter! You have a +pi/2 phase shift in one case and a -pi/2 phase shift in the other, which gives you the difference you see.

I roughly sketched the math behind that half an eternity ago here: https://www.physicsforums.com/showpost.php?p=2241460&postcount=8.

It is a bit rough, but gives a good idea of what is happening.