I Quantum eraser experiment

[J O Linton]

TL;DR Summary

I wish to know what QT predicts in the case of a quantum eraser experiment using a M-Z interferometer

The diagram above shows an ideal perfectly collimated equal arm M-Z interferometer. Photons enter the apparatus at the bottom left at a rate of 100 vertically polarised photons every second. Ideal polarisers are placed in the arms A and B at 45 degrees left and right. A third polariser is placed in arm C. I wish to know the expected rate of detection of photons at the two detectors D1 and D2 under the following conditions: of the third polariser: 1) Absent 2) Veritcal 3) inclined at 45 deg and 4) horizontal.
My (limited) understanding of QM leads me to expect the following results:
1) (Absent) D1: 25, D2: 25 (i.e. no interference)
2) (Vertical) D1: 50, D2: 25 (i.e. constructive interference in arm C (shoulkd D1 be 25?)
3) (Inclined) D1: 12.5 D2: 25 (i.e. no interference)
4) (Horizontal) D1: 50, D2: 25 (i.e. constructive interference in arm C (shoulkd D1 be 25? or perhaps 0?)
Are these expectations correct? If not, what should they be and why?

 

[pines-demon]

TL;DR Summary: I wish to know what QT predicts in the case of a quantum eraser experiment using a M-Z interferometer

View attachment 363249
The diagram above shows an ideal perfectly collimated equal arm M-Z interferometer. Photons enter the apparatus at the bottom left at a rate of 100 vertically polarised photons every second. Ideal polarisers are placed in the arms A and B at 45 degrees left and right. A third polariser is placed in arm C. I wish to know the expected rate of detection of photons at the two detectors D1 and D2 under the following conditions: of the third polariser: 1) Absent 2) Veritcal 3) inclined at 45 deg and 4) horizontal.
My (limited) understanding of QM leads me to expect the following results:
1) (Absent) D1: 25, D2: 25 (i.e. no interference)
2) (Vertical) D1: 50, D2: 25 (i.e. constructive interference in arm C (shoulkd D1 be 25?)
3) (Inclined) D1: 12.5 D2: 25 (i.e. no interference)
4) (Horizontal) D1: 50, D2: 25 (i.e. constructive interference in arm C (shoulkd D1 be 25? or perhaps 0?)
Are these expectations correct? If not, what should they be and why?

This question is weird, clearly the polarizer at C has much to do with anything. As you say D2 always receives 25% of photons, and 25% goes to branch C, the rest are killed by the polarizers at A and B. The 25% that go to branch C are vertically polarized again, so:

• no polarizer, D1 receives the full 25% of photons.
• vertically polarized, D1 receives the full 25% of photons.
• horizontally polarized, D1 receives no photons
• inclined 45°, D1 receives half of the 25%.

Interference happens at the beam splitter so has nothing to do with branch C or D1.
Also these calculations have nothing to do with quantum mechanics and can be predicted using wave optics.

 

[J O Linton]

Thank you for your response. I now realise that classical wave theory and QM must give the same answers as to the frequency of detection. It was stupid of me to suggest that D1 could ever fire 50% of the time! The quantum weirdness only becomes apparent when you try to explain why you get the same results even when there is only one photon in the apparatus at any one time.

Just one thing about your results. I specified that the phtons enter the apparatus vertically polarized. Surely this means that when the polariser in arm C is vertical D1 should fire 25% and when it is horizontal it will not fire at all? Your results seem to be the other way round.

 

[pines-demon]

Just one thing about your results. I specified that the phtons enter the apparatus vertically polarized. Surely this means that when the polariser in arm C is vertical D1 should fire 25% and when it is horizontal it will not fire at all? Your results seem to be the other way round.

Sorry you are right, it exits vertically again, I was miscalculating the shift due to the beam splitter mirrors in the figure. I edited my post.