= Question 2: A second proof of beam splitter relations Suppose we know that the input operators a1, az satisfy: ( [ai,

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Question 2 A Second Proof Of Beam Splitter Relations Suppose We Know That The Input Operators A1 Az Satisfy Ai 1 (63.09 KiB) Viewed 29 times

= Question 2: A second proof of beam splitter relations Suppose we know that the input operators a1, az satisfy: ( [ai, a ] = dij (+) { [aż,aj] = 0 i,j E {1,2} ( [at, a.] = 0 We wrote a beam splitter as: (ti (az.) = ; 2) (a) Define: = = (n = ata, input photon number operators: lñz = a az înze = ata, output photon number operators : (ñiz: = a, az! Assume that the total number of photons is conserved (the beam splitter doesn't generate nor destroy photons), înai + în2 = îy' + ñz'. a. Prove: 17112+ |t112 = 1 = [r212 + tz12 ritz + tir2 = 0 b. Prove that (*) holds for the output states.