Modified Mach-Zehnder Interferometer

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The Mach-Zehnder interferometer's operation is clarified, noting that removing the second beamsplitter leads to direct photon paths to the detectors without interference. It is mentioned that photon counting data, such as the efficiency of the first beamsplitter, is typically reported in scientific papers. When one detector is removed, the remaining detector still registers approximately 50% of the photons, as the removal does not affect the measurement at the other detector. References to foundational works, like Young's principles of optics, are suggested for further reading. The discussion emphasizes the importance of published counts in understanding photon behavior in interferometers.
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The Mach-Zehnder interferometer is shown in wikipedia and on David Harrison's page.

If the second (upper right) half silvered mirror is taken away and no sample (as in the wikipedia setup) is in any of the two paths, I read that when sending individual photons through the device, roughly 50% of them end up in each detector.

What I would like to know is the following:
  1. Does anyone know a paper where real counts are reported, e.g. like: "we send 100 individual photons, 49 ended up in 1 and 47 ended up in 2, 4 where lost"?
  2. If I further remove one of the detectors, what percentage of photons is registered in the remaining detector? (published counts available?)

Thanks,
Harald.
 
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1. Removing the second beamsplitter eliminates the interference and just let's the two beams from the first beamsplitter go directly to the detectors. The photon counting you are asking for is done when the efficiency of the first beamsplitter is measured (ignoring the reflectivity of the two mirrors). That is often reported in papers describing interferomters.

2. If 50% goes to each detector, then 50% will still go to the remaining detector. Removing one detector has no effect on what's measured at the other detector.
 
Young's work may be a good starting point.
Mach E., The principles of physics optics
New York - Dover, 1953
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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