Dynamics of a non-linear Jaynes-Cummings model

Abstract

A non-linear Jaynes-Cummings model is presented. The atom interacts with two modes non-linearly. One- and multiphoton processes are considered. The Heisenberg equations of motion are solved exactly with detuning present. The evolution operator is calculated for the general case. Different statistical quantities pertaining to either the atom or the fields are computed. Numerical investigations are carried out for the phenomena of collapses and revivals, bunching and antibunching, modes correlation and squeezing for different initial values of the mean number of photons