Question about Interference Patterns in Kim Delayed Choice Eraser

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Discussion Overview

The discussion revolves around the delayed choice quantum eraser experiment as described in the paper by Kim et al. Participants are trying to understand the mathematical and conceptual basis for the interference patterns observed, particularly focusing on the phase shift between different detection paths of idler photons and its implications for signal photon patterns.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in understanding the mathematical derivation of interference patterns R_01, R_02, R_03, and R_04, specifically questioning the source of the pi phase shift between R_01 and R_02.
  • Another participant suggests that the beam splitter creates a path difference due to reflection versus transmission, and notes that the deviation angle of the idler photon from the prism may introduce phase differences, although this may not explain the constant phase difference observed.
  • A different participant outlines the paths to detectors D1 and D2, indicating that both paths involve a combination of beam splitter transmissions and reflections, and questions whether the interference is due to differences in polarization affecting the destructive interference observed.
  • One participant highlights the importance of phase signs, noting a +pi/2 phase shift in one case and a -pi/2 phase shift in another, which contributes to the observed differences in interference patterns.
  • A participant references a previous sketch of the math related to these phase shifts, indicating that it provides insight into the phenomena being discussed.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and interpretations regarding the source of phase shifts and the implications for interference patterns. No consensus is reached on the exact mechanisms or explanations for the observed phenomena.

Contextual Notes

Participants acknowledge the complexity of the mathematical functions involved and the need for further clarification on the relationships between the idler photon properties and the resulting interference patterns.

msumm21
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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!
 
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msumm21 said:
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
 
Last edited:
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.
 
msumm21 said:
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.
 

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