Quasiprobability distributions for the cavity-damped Jaynes-Cummings model with an additional Kerr medium

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Abstract
A cavity-damped Jaynes-Cummings model with a Kerr-like medium filling the cavity is investigated in the rotating-wave approximation. We introduce six operators with respect to the light field whose equations of motion are transformed to six coupled partial differential equations using the s-parametrized quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882 (1969)]. Equations of motion for expansion coefficients of the distribution functions are solved by a Runge-Kutta procedure for vector tridiagonal relations. Starting with an initial coherent state for the cavity field and the atom in its upper state, we find that revivals of the atomic inversion are more pronounced for a given damping constant compared to the case of no Kerr medium. Also, quadrature squeezing is less affected by weak cavity damping and thermal noise compared to the standard Jaynes-Cummings model. The effect of damping on interesting non-Gaussian structures is also discussed.