Mathcad - RamseyInterferometer - Users.csbsju. edu

The Ramsey Atomic InterferometerFrank RiouxThe Ramsey interferometer, which closely resembles the Mach-Zehnder interferometer, is constructedusing two /2 Rabi pulses (R1 and R2) separated by a phase shifter in the lower arm, as shownbelow.wheree10 g 01The matrix representations of the phase shifter and the Rabi elements are as follows:PhaseShift100e iRabicos 2sin 2sin 2cos 2Rabi2 0.707 0.7070.7070.707 The input to the interferometer is the upper state |e> of a two-state atom. The first pulse behaveslike a Hadamard gate creating a coherent superposition of |e> and the lower state of the atom, |g>.Rabi2 1 0 112 2 2112 2 21211The phase shifter alters the superposition by adding a phase to |g>.PhaseShift Rabi2 10112 2 2112 ei 2 2121e iIn the absence of a phase shift ( = 0) the two /2 pulses behave like a not gate yielding |g> at theoutput channel.Rabi2 PhaseShift 0( ) RabiHowever if = , the interferometer is equivalent to the identity operator and the output is |e>.Rabi2 PhaseShiftRabi22 10100110

In general, the result is a superposition of |e> and |g>.Rabi2 PhaseShiftRabi2 10121212 ei 12 ei eg=121 e i1 e iThe probabilities of detecting |e> and |g> at the output channel depend on the phase , exhibitinginterference effects as in the Mach-Zehnder interferometer with a phase shifter in the lower arm. Thisis shown below both algebraically and graphically.P e10TRabi2 PhaseShift Rabi2 102 simplify1212 cos P g 01TRabi2 PhaseShift Rabi2 102 simplify1212 cos 0 .01 4P e10.5P g00 1 2 3 4