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- How do different polarizers added in a MZI change the interference pattern?

I have a question on how exactly polarizing filters would influence interference in a Mach-Zehnder interferometer.

To explain, I'll show some configurations and what I would expect to happen - please tell me if I am incorrect anywhere.

Here is the standard MZI configuration with no filters and a single-photon source on the lower left

In this configuration, 100% of photons will reach D1, none will reach D2, due to the differential phase shifts from the beam splitter. (I assume that both beam splitters are symmetric and shift transmitted and reflected by 90°, as explained here: https://www.physicsforums.com/threa...h-zehnder-interferometer.972867/#post-6188472)

Now I add two polarizing filters, one vertical, one horizontal

In this configuration (with single photons emitted from the light source on the lower left), on average, only every second photon will hit one of the detectors (for simplicity, assume that the light source emits photons with polarization 45°, i.e. a superposition og horizontal and vertical). Of these 50%reach D1, 50% reach D2 because the polarization adds a "which-path information" to the photon state and thus destroys the interference pattern. So overall I have 25% at D1, 25% at D2, 50% lost.

When I now add a third filter at 45° in the D1-path

I expect that this destroys the which-path information. However, the which-path information is still available at D2, so I would expect now that I have 25% of the photons at D2, 12,5% at D1 (number is halved due to the loss at the third filter).

And finally, I add a filter to the D2-path:

Now I've destroyed the which-path information on both paths, so that interference should work again. In this situation I would expect 25% of the photons to end up at D1, none ending up at D2 and the rest being absorbed at one of the filters.

Are all these considerations correct or did I make a mistake somewhere?

To explain, I'll show some configurations and what I would expect to happen - please tell me if I am incorrect anywhere.

Here is the standard MZI configuration with no filters and a single-photon source on the lower left

In this configuration, 100% of photons will reach D1, none will reach D2, due to the differential phase shifts from the beam splitter. (I assume that both beam splitters are symmetric and shift transmitted and reflected by 90°, as explained here: https://www.physicsforums.com/threa...h-zehnder-interferometer.972867/#post-6188472)

Now I add two polarizing filters, one vertical, one horizontal

In this configuration (with single photons emitted from the light source on the lower left), on average, only every second photon will hit one of the detectors (for simplicity, assume that the light source emits photons with polarization 45°, i.e. a superposition og horizontal and vertical). Of these 50%reach D1, 50% reach D2 because the polarization adds a "which-path information" to the photon state and thus destroys the interference pattern. So overall I have 25% at D1, 25% at D2, 50% lost.

When I now add a third filter at 45° in the D1-path

I expect that this destroys the which-path information. However, the which-path information is still available at D2, so I would expect now that I have 25% of the photons at D2, 12,5% at D1 (number is halved due to the loss at the third filter).

And finally, I add a filter to the D2-path:

Now I've destroyed the which-path information on both paths, so that interference should work again. In this situation I would expect 25% of the photons to end up at D1, none ending up at D2 and the rest being absorbed at one of the filters.

Are all these considerations correct or did I make a mistake somewhere?

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