A resonant two-photon extension of the Jaynes–Cummings model is described by the effective…

A resonant two-photon extension of the Jaynes–Cummings model is described by the effective Hamiltonian Heff = h_(aˆ 2_ˆ+ + aˆ 2† _ˆ_), where, for the sake of simplicity, a small Stark shift term has been ignored. This Hamiltonian represents two-photonabsorption and emission between atomic levels of like parity. The process is represented by Fig. 4.13, where the broken line represents a virtual intermediate state of opposite parity.  (a) Obtain the dressed states for this system.  (b) Obtain the atomic inversion for this model assuming the atom initially in the ground state and that the field is initially in a number state. Repeat for a coherent state. Comment on the nature of the collapse and revival phenomena for these states.  (c) Obtain the atomic inversion for an initial thermal state.

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