(Solved) : 5 6 Points Consider Qubit States 9 E Energies U U Energy Separation U U Hwg Assume Ue U Q Q44060720 . . .
5) (6 points) Consider a qubit with states 9), e) having energies U,, U, and energy separation U-U, = hwg. Assume Ue > U,. The qubit is illuminated with radiation at frequency w where W-W, = A, and assume A > 0. The radiation couples the two levels through the electric dipole Hamiltonian Hei = -dE = – d e -wt + etwt). For this problem we will neglect the polarization of the field, assume E = E*, and use the Rabi frequency 2 = Edeg/h with deg = (eld g) to characterize the strength of the qubit-radiation coupling. a) Assume at t=0 the qubit state is ) = 9). Give a formula for the probability to be in state le) as a function of time t using the Schrödinger equation solution (Rabi oscillations). b) Assume at t=0 the qubit state is 4) = 9). Give a formula for the probability to be in state le) as a function of time t using first order time dependent perturbation theory and the rotating wave approximation. c) Same as b) but do not make the rotating wave approximation. d) Compare the results found in a), b), and c) for short times such that t < 1, At < 1, and wet <1. If the results are not all the same explain why. Show transcribed image text 5) (6 points) Consider a qubit with states 9), e) having energies U,, U, and energy separation U-U, = hwg. Assume Ue > U,. The qubit is illuminated with radiation at frequency w where W-W, = A, and assume A > 0. The radiation couples the two levels through the electric dipole Hamiltonian Hei = -dE = – d e -wt + etwt). For this problem we will neglect the polarization of the field, assume E = E*, and use the Rabi frequency 2 = Edeg/h with deg = (eld g) to characterize the strength of the qubit-radiation coupling. a) Assume at t=0 the qubit state is ) = 9). Give a formula for the probability to be in state le) as a function of time t using the Schrödinger equation solution (Rabi oscillations). b) Assume at t=0 the qubit state is 4) = 9). Give a formula for the probability to be in state le) as a function of time t using first order time dependent perturbation theory and the rotating wave approximation. c) Same as b) but do not make the rotating wave approximation. d) Compare the results found in a), b), and c) for short times such that t
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Answer to 5) (6 points) Consider a qubit with states 9), e) having energies U,, U, and energy separation U-U, = hwg. Assume Ue > U…
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