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Unformatted text preview: HOMEWORK ASSIGNMENT 10 PHYS852 Quantum Mechanics II, Spring 2008 1. Dark State Adiabatic Passage: [Should be fairly easy] An atomic system consists of two ground state hyperfine sublevels couple via an electronically excited state. Let  1 ) and  2 ) refer to the two lower levels and  e ) be the upper level. If  1 ) corresponds to an m f = 1 state,  e ) to an m f = 0 state, and  2 ) to an m f = 1 state, then due to angular momentum conservation, a rightcircularly polarized laser will couple  1 ) to  e ) and a leftcircularly polarized laser will couple  2 ) to  e ) . In this way, the following Hamiltonian can be realized (in a suitable rotating frame and in the rotating wave approximation): H = i planckover2pi1  e )( e  + planckover2pi1 R (  1 )( e  +  e )( 1  ) + planckover2pi1 L (  2 )( e  +  e )( 2  ) , (1) where the i planckover2pi1 term gives the excited state a finite lifetime due to spontaneous emission. Ignoring the fact that H is not Hermitian, find the eigenvalues and eigenvectors of H . In general, the eigenvalues will be complex, of the from n i n . Then we can think of n as the inverse lifetime of the eigenstate before it decays due to spontaneous emission. We want to consider the socalled counterintuitive pulse sequence, where the system starts out in state  1 ) , with R = 0 and L = . Then R is slowly increased and L is decreased, maintaining 2 R + 2 L = 2 . Plot the real parts of the eigenvalues versus R during this pulsesequence. If the two Rabifrequencies are varied very slowly, what will the final state of the system be? What is thetwo Rabifrequencies are varied very slowly, what will the final state of the system be?...
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This note was uploaded on 11/26/2010 for the course PHYSICS PHYS 852 taught by Professor Michaelmoore during the Spring '10 term at Michigan State University.
 Spring '10
 MichaelMoore
 mechanics, Work

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