Mach–Zehnder interferometer question, path detection

In summary, the Mach-Zehnder interferometer can measure which path the beam took by measuring the change in momentum of the (fully silvered) mirrors, but this information is usually hidden and is not detectable using "weak measurements."
  • #1
msumm21
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In a Mach–Zehnder interferometer experiment, can you measure which path the beam took by measuring the change in momentum of the (fully silvered) mirrors (i.e. if path A was taken then the mirror on path A was "pushed" a bit, if path B was taken then the mirror on path B was "pushed" a bit)?
 
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  • #2
msumm21 said:
In a Mach–Zehnder interferometer experiment, can you measure which path the beam took by measuring the change in momentum of the (fully silvered) mirrors (i.e. if path A was taken then the mirror on path A was "pushed" a bit, if path B was taken then the mirror on path B was "pushed" a bit)?

i don't know if the path can be found out via push on the mirrors...

however

there are a couple of other ways to find out which path (in mach-zehnder, double-slit, delayed erasure etc) the photon/beam took.

the interference does not happen when the path is "found out"/known
 
  • #3
The reason I ask is because every time the experiment is done it would seem like the which-path information would be encoded in the momentum of the mirrors, and theoretically you could always go back and look at the momentum of the mirrors to see which path was taken, but then doesn't QM say there is no interference if that is the case?

Somehow the beam always goes into the same detector (there is interference) so evidentially the momentum of the mirrors is hidden somehow? I think I am missing something basic here.
 
  • #4
In order to really measure the change in momentum induced by the photon, the initial momentum uncertainty of the mirror should be small compared to the momentum of the photon. Otherwise the momentum transfer is not detectable in principle. In any typical realization of a Mach-Zehnder interferometer the mirror momentum uncertainty is too large to allow which-way measurements utiliziung the momentum transfer by the photon.
 
  • #5
Theoretically (maybe this is not possible in practice) if you very precisely knew the momentum of the mirrors before the experiment, would the interference then not occur? So if you know the momentum of the mirrors well then the beam could pass to either detector?

Thanks for the info Cthugha.
 
  • #6
Right, if you prepared the mirrors in a VERY precise momentum state (and therefore a very unprecise position state via the Uncertainty principle), you would not see the interference, because the position of the mirrors would be out of wack!
 
  • #7
msumm21 said:
In a Mach–Zehnder interferometer experiment, can you measure which path the beam took by measuring the change in momentum of the (fully silvered) mirrors (i.e. if path A was taken then the mirror on path A was "pushed" a bit, if path B was taken then the mirror on path B was "pushed" a bit)?
If you are able to detect a change in the mirror, then the quantum state of the mirror after the income of the photon must be significantly different from that before the income of the photon. In that case, these two states of the mirror are nearly orthogonal, i.e., their scalar product is close to zero. But that means that the mirror causes decoherence of the photon state, which means that interference is destroyed.

Conversely, if you can see interference, then it means that there is no decoherence, and consequently that you are not able to detect a change in the mirror.

This is discussed more quantitatively in the book
B. Schumacher, B. D. Westmoreland: Quantum Processes, Systems, and Information (2010)
 
  • #8
Demystifier, have the "weak measurements" you always talk about been done for the Mach–Zehnder interferometer experiment?
 

1. What is a Mach-Zehnder interferometer?

A Mach-Zehnder interferometer is an optical device that uses interference patterns to measure small changes in the optical path length between two beams of light. It consists of two beamsplitters and two mirrors arranged in a specific configuration.

2. How does a Mach-Zehnder interferometer work?

In a Mach-Zehnder interferometer, a beam of light is split into two paths by the first beamsplitter. The two beams then travel through different paths and are recombined at the second beamsplitter. The resulting interference pattern is then detected and analyzed to measure changes in the optical path length.

3. What is the purpose of path detection in a Mach-Zehnder interferometer?

Path detection in a Mach-Zehnder interferometer is used to measure the changes in the optical path length caused by external factors such as temperature, pressure, or refractive index. This information can then be used to make precise measurements or detect small changes in the environment.

4. What are the advantages of using a Mach-Zehnder interferometer over other interferometers?

The Mach-Zehnder interferometer offers a number of advantages over other interferometers, including high sensitivity, low noise, and the ability to measure changes in the optical path length without needing a reference beam. It also allows for easy alignment and can be used for a wide range of applications.

5. What are some common applications of the Mach-Zehnder interferometer?

The Mach-Zehnder interferometer is commonly used in fields such as telecommunications, metrology, and sensing. It can be used to measure small changes in temperature, pressure, and refractive index, as well as to detect vibrations and movements in structures, and to analyze the properties of materials.

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