MIT OpenCourseWarehttp://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Time development of a coupled two level system The Hamiltonian for this case is: Given that you start in state |a>, what is the time-dependent probability of ending up in state |b>? Frequency splitting: Δ := 1 Rabi frequency: Ω V := V2 + 2 Note here I have expressed energy () Δ as inverse time. E/hbar ⎡ V2 ⎤ 2Pt V) :=⎢ ⎥⋅ ( ()t( , sin Ω V ⋅ )⎢ 2 2 ⎥ ⎣(V + Δ )⎦ iDefine a time grid: i := 0 .. 500 τ :=i 50 Calculate probabilities for different values of the coupling: V/∆ = 0.1, 0.5, 1, 5 P1i := P(τi, 5) P2i := P(τi, 1) P3i := P(τi, 0.5) P4i := P(τi, 0.1) P1 0.8 P2 0.6 P3 0.4 P4 0.2 0 0 1 2 3 Δ τ⋅ π 0.1 0.08 P3 0.06 P4 0.04 0.02 0 0 1 2 3 Δ τ⋅
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