Question

Course Exam 1 Exam 1 Problem 4

Problem 4
Midterm Exam due Nov 5, 2020 22:30 IST
Part A
4.0 points possible (graded, results hidden)

Consider a Mach-Zehnder interferometer in which the matrices representing the beam splitters BS1 and BS2, denoted as B1 and B2, respectively, are given by
B1=12–√(−1111),B2=12–√(i−i11).


Consider beam splitter 2 acting on a state ψ=(αβ). What is the square norm of the resulting state B2ψ?

Write your answer in terms of alpha for α and beta for β. As α and β are complex numbers, you may use functions such as abs(), re(), im() and conj() to manipulate them.

|B2ψ|2=
unanswered

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Part B
8.0 points possible (graded, results hidden)

Consider a photon that enters the interferometer as labeled by the “incident beam" in the figure, with state (10). What are the probabilities P0 and P1 for detection in D0 and D1 respectively?

P0= unanswered

P1= unanswered

If the lower branch of the interferometer is blocked, what are the (absolute) probabilities P0 and P1 for detection in D0 and D1 respectively, and what is the probability for the photon to be blocked?

P0= unanswered

P1= unanswered

Pblocked= unanswered

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Part C
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Why doesn't this Mach-Zehnder interferometer work to discover functional Elitzur-Vaidman bombs without detonating them by inserting them on the lower branch?

Because with functioning bombs, photons always go to D0, but with nonfunctioning bombs, photons can go to either D0 or D1
Because with functioning bombs, photons always go to D1, but with nonfunctioning bombs, photons can go to either D0 or D1
Because with nonfunctioning bombs, photons always go to D0, but with functioning bombs, photons can go to either D0 or D1
Because with nonfunctioning bombs, photons always go to D1, but with functioning bombs, photons can go to either D0 or D1
Because with both functioning and nonfunctioning bombs, photons can go to either D0 or D1
Because with functioning bombs, photons never reach a detector
Because with nonfunctioning bombs, photons never reach a detector
Because functioning bombs always explode
unanswered

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Part D
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To make this Mach-Zehnder interferometer work, we will insert a phase shifter with phase eiδ to the upper branch (see figure) in order to have every incident photon emerge into D0 when both branches of the interferometer are operational.

Find the phase α for the photon state ψ=12√(eiα1) that incident on BS2 will definitely go into D0. Give your answer as an angle α∈(−π,π].

α=
unanswered

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Part E
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Find the required phase δ of the phase shifter (δ∈(−π,π]).

δ=
unanswered

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Answer 1

Answer:

Wt s this yaar... lol