Question: Consider the Mach-Zehnder interferometer shown in Fig. Assume it has 20-80 beam splitters so that 20% of the light is reflected through each beam splitter while 80% of the light is transmitted.
a. Find
i. The probability amplitude for a photon to be reflected by the beam-splitter.
ii. The probability amplitude for a photon to be transmitted by the beam-splitter.
iii. The probability for a photon to go from A to B through arm 1 if arm 2 is blocked.
b. If the arms of the interferometer have the exact same length and both arms are unblocked:
i. Find the probability of a photon going from A to B if the arms are distinguishable.
ii. Find the probability of a photon going from A to B if the arms are indistinguishable.
c. If the wavelength of the light is 500 nm and the number of photons incident on the interferometer per second is N = 1000, make a graph showing the number of photons detected at B in 1 s as a function of the difference between the lengths of the two arms. Your graph must have:
i. A curve similar to what you would get in the lab.
ii. Scale for the vertical axis.
iii. Scale for the horizontal axis.
