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I am tying to understand the working of Mach-Zehnder Interferometer in the physical sense (how it behaves and why it does so etc.). The source I am referring to is this: (https://www.cs.princeton.edu/courses/archive/fall06/cos576/papers/zetie_et_al_mach_zehnder00.pdf)

In this source there are a couple of definitions that are confusing me like anything: "..We shall use the following definitions: $l_1$ and $l_2$ are the total path lengths for the light travelling from the source to the detector for the upper and lower paths respectively."

Doubt 1: When it says 'from source to the detector' there are two detectors! And it is never explicitly states that the distance from the second beam splitter to the two detectors $A$ and $B$ is equal. It doesn't have to be! Does the author implicitly assume that in the paper and its not the generic case? Or its the generic case and I am missing something?

Doubt 2: This paper is talking in terms of phase difference for paths to detector $A$ and $detector B$ and calculating that. I understand this part. But, how do we calculate the probabilities of a photon arriving at detector $A$ and $B$ if we know the values of phase difference in each case? [Again I am looking for the generic case calculations - both for phase difference and probabilities]?

Can someone please clarify?

P.S. My background is in CS so please take that into consideration.

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Doubt 1: In general for an MZI it is assumed that the paths have equal length. The considered lenght is the one between the two BSs.

Doubt 2: Phase difference introduces a relative phase in the state of the quantum of light inside the interferometer and can be probed/correct using the probabilities that arise from the detectors.

One encode quantum information in this device as the path information: $\vert 0 \rangle $ for instance can be described by the state $\vert 01 \rangle$ that corresponds to the fact that the photon took the lower arm path and $\vert 1 \rangle$ the other way around. After the beam-splitter the photon will be in superposition of the two path-choices $\alpha \vert 01 \rangle + \beta \vert 10 \rangle$ with $\alpha^2+\beta^2=1$ and a phase-shifter or a difference in phase in the paths introduces a relative phase $e^{i\phi}$ that can be either fixed, probed, or made to vary for finding specific quantities of interest, such as the interferometric visibility.

The fact that they talk about the phase difference is associated in quantum information to the fact that global phases do not matter for the description of quantum states.

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  • $\begingroup$ thank you. just to reiterate as i understand the 'path length' is by default considered the length b/w 2 BS so i think the definition should be edited accordingly. thanks for clarifying. I am still unclear about the second one though. I understand the calculation of the 'phase difference' and its final value b/w for each of the two detectors. But I am unclear about the part: ".. paths introduces a relative phase eiϕ that..". can you provide an explicit description of how to calculate the probability for each detector given the value of the phase difference for each (as in paper above)? $\endgroup$
    – TheoryQuest1
    Commented Jul 24, 2022 at 17:18
  • $\begingroup$ I do understand the concept, but not how its calculated explicitly give the phase difference value.. thanks in advance $\endgroup$
    – TheoryQuest1
    Commented Jul 24, 2022 at 17:19

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