Squeezed vacuum states in a nonlinear medium modulated by periodic kicking

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Abstract
In this paper we study the dynamics of a nonlinear quantum-optical system subjected to a periodic modulation in the form of kicks. The system consists of a nonabsorbing anharmonic medium related to optical bistability, a degenerate parametric amplifier with a classical pump field that is modulated by a periodic sequence of kicks, and the initial state is taken to be a squeezed vacuum state. Using the related SU(1,1) coherent states (which are squeezed vacuum states), we study and compare the quantum and classical dynamics of the system. The ‘‘classical’’ motion in this case means the motion projected onto the phase space defined by the parameter labeling the generalized coherent states. For certain values of the coupling constants, we obtain both regular and chaotic motion in the classical phase space. In the quantum dynamics of the system, the manifestation of the classical chaos turns out to be rather weak, at least in the regime numerically accessible to us. We study the time evolution of the initial-state population probability, the average photon number in the field, and the squeezing of the field. We also briefly discuss the level statistics of the evolution operator.

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