Question: Consider the Mach-Zehnder interferometer shown in Fig. It has 50-50 beam splitters, which reflect 50% of the intensity of the light incident on them and transmit the other 50%.
a. Find the probability of transmission through a 50-50 beam splitter.
b. Find the magnitude of the probability amplitude of going through the beam splitter.
c. The probability amplitude of going through the two beam splitters is the product of the individual probability amplitudes. What is the magnitude of the probability amplitude for going from A to B when arm 1 is blocked?
d. What is the probability of a photon to go from A to C when arm 2 is blocked?
e. If the two paths of the interferometer are distinguishable,
i. What is the probability of going from A to B when neither arm is blocked?
ii. What is the probability of going from A to C when neither arm is blocked?
f. If the paths through the interferometer are indistinguishable,
i. What is the probability for a photon to go from A to B when φ = 3π?
ii. If 500 photons per second are incident to the interferometer from A, how many photons reach B in 1s when φ = 3π/2?
iii. If 500 photons per second are incident to the interferometer from A, how many photons reach B when φ = 3π?
iv. Based on the previous question, how many photons reach C in 1 s when φ = 3π?
v. If 500 photons per second are incident to the interferometer from A, what is the value of φ if 250 photons reach B in 1 s?