Question

Consider the better bomb tester experiment shown on the previous page. This is a bomb placed in a Ring interferometer. Both beam splitters are identical and have real transmissivities |T1| = |T2| = T and reflectivities |R1| = |R2| = R. The arm between the two beam splitters that includes the bomb has length L0, while the full length of the ring is L. This means that the field E4 travels a distance L - L0 before becoming E5, the input to the initial beam splitter. (a) In parts (a)-(f), assume that the bomb is faulty so that the field simply passes through the bomb. Find equations for E1 and E6 in terms of E0 and E5. (b) Find equations for E3 and E4 in terms of E2. (c) As the wave travels down the path, it picks up a phase of e^(ikx) where x is the distance traveled. This transforms E2 = E1e^(ikL0), and E5 = E4e^(ik(L-L0)). Perform the above substitutions in the two equations you found in part (a) and the two equations you found in part (b). (d) Solve this set of four equations to find the output fields E3 and E6, each in terms of E0 only. (e) With the above two equations, show that P3 = (|E3|^2) / (|E0|^2) = (T^4) / (1 + R^4 + 2R^2cos(kL)) and P6 = (|E6|^2) / (|E0|^2) = (2R^2[1 + cos(kL)]) / (1 + R^4 + 2R^2cos(kL)). (f) At what value of φ = kL is P6 = 0? This is equivalent to saying the probability of detecting a single-photon is zero for small |E0|. (g) Now assume the bomb is live so that the fields will be blocked by the bomb. We also assume that the length L satisfies the phase shift of part (f). In this case, why are P3 = (|E3|^2) / (|E0|^2) = 0 and P6 = (|E6|^2) / (|E0|^2) = R^2? (h) What is the probability that the bomb will detonate? Given this probability and P6, do we want large R or small R?

          Consider the better bomb tester experiment shown on the previous page. This is a bomb placed in a Ring interferometer. Both beam splitters are identical and have real transmissivities |T1| = |T2| = T and reflectivities |R1| = |R2| = R. The arm between the two beam splitters that includes the bomb has length L0, while the full length of the ring is L. This means that the field E4 travels a distance L - L0 before becoming E5, the input to the initial beam splitter.
(a) In parts (a)-(f), assume that the bomb is faulty so that the field simply passes through the bomb. Find equations for E1 and E6 in terms of E0 and E5.
(b) Find equations for E3 and E4 in terms of E2.
(c) As the wave travels down the path, it picks up a phase of e^(ikx) where x is the distance traveled. This transforms E2 = E1e^(ikL0), and E5 = E4e^(ik(L-L0)). Perform the above substitutions in the two equations you found in part (a) and the two equations you found in part (b).
(d) Solve this set of four equations to find the output fields E3 and E6, each in terms of E0 only.
(e) With the above two equations, show that P3 = (|E3|^2) / (|E0|^2) = (T^4) / (1 + R^4 + 2R^2cos(kL)) and P6 = (|E6|^2) / (|E0|^2) = (2R^2[1 + cos(kL)]) / (1 + R^4 + 2R^2cos(kL)).
(f) At what value of φ = kL is P6 = 0? This is equivalent to saying the probability of detecting a single-photon is zero for small |E0|.
(g) Now assume the bomb is live so that the fields will be blocked by the bomb. We also assume that the length L satisfies the phase shift of part (f). In this case, why are P3 = (|E3|^2) / (|E0|^2) = 0 and P6 = (|E6|^2) / (|E0|^2) = R^2?
(h) What is the probability that the bomb will detonate? Given this probability and P6, do we want large R or small R?

consider the better bomb tester experiment shown on the previous page this is a bomb placed in a ring interferometer both beam splitters are identical and have real transmissivities t1 t2 t 32737

Added by Shannon D.

Question

Please give Ace some feedback