Regular and Chaotic Coherent State Dynamics of Several Quantum Optical Models
Alexander V. Gorokhov, Elena V. Rogacheva, Alexander V. Shiryaev
Abstract
The coherent state representations of the group G = W1 G0 (where G0 = SU(2), SU(1,1)) are used in computer simulation of the dynamics of single two-level atom (G0 = SU(2)) interacting with a quantized photon cavity mode - the Jaynes - Cummings model (JCM) without the rotating wave approximation and, in general, nonlinear in photon variables). The second case (hyperbolic Jaynes - Cummings model (HJCM), G0 = SU(1,1)) corresponds to the quantum dynamics of quadratic nonlinear coupled oscillators (the parametric resonance on double field frequency and a three - wave parametric processes of nonlinear optics). Quasiclassical dynamical equations for parameters of approximately factorizable coherent states for these models are derived and regimes of motion for "atom" and field variables are analyzed.
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