Question

Problem 3 The Mach-Zehnder Interferometer Consider the interferometer set up shown in the diagram. A single photon source impinges on n the first (50/50) beam splitter BSi, after which the photon rellects off inlrrors Mi and/or Az, and converge on the second beam splitter BS2 The photon is measured at either detector Di or D. To keep the annlysis simple, all segments are con- sider to be equal length (thus traveling the upper route is the same distance as the lower route). A phase shifter, φ, is present in the lower ann, shin. ing the lower portion of the state by e. For now we set ф-0°. One important feature, which we should have covered back in optics: when the pho- ton refiects (but not transmitted straight through) at elther nirror or beam splitter the phase 1s shifted by 5, i.c a factor of et nultiplies. souree the state. Di BS2 BSi a) Find the overall state of the photon after BS2 Calculate the probability for the plioton to be detected at Di and the probability to be detected at Da (which ts just 1 mius the probability at Di) b) What value of φ results in the probability to be l for the photon to be gletected at D2 and 0 at D?

there are two parts in this problem please provide complete detailed solution to each part of this problem separately

Answer 1

D 2. Da BS-2 Sop mede i Fot a smmuhic loscles beam yelittert, the Beam sli lut matrix is iren y 8S-1 PS T openabrt mam for 8s1 and 8S-1 are same and eual to B. uang Heisenberg The fare, the pichuhe, an initial danki shan passing beam s ti He t-土.( B, is Φ opesahrt for BS-4 ) 어 사en it Pam eo thhough ^Phare shifter (PS), it's stati ф bahseon the two-paths . Again, when the beam-Par ea Hungh BS-2, it's stata chall becoma cing eq 4 the final talin う18 24 6 4 t e The diagomal elamunts spmesens tha prebabiehy that tha photon wi e mea D whid-in-the output- of each pert (l+ e'ㅇㄴ ㄧ一(1-eigリし.ei milan..一Pa, P, () so that f2-1 and Pa : O e hare to find ISo so thot no Hena, the phas chift shonld be photons ans de cted at D2