Entropy and variance squeezing of two coupled modes interacting with a two-level atom: Frequency converter type

A modified Jaynes-Cummings model which consists of a two-level atom interacting with two modes of the electromagnetic field is introduced. More precisely we have considered a Hamiltonian model that includes two types of interaction: One is the field-field (frequency converter type) and the other is the atom-field interaction. By invoking a canonical transformation an exact solution of the wave function in the Schrödinger picture is obtained. The result presented in this context is used to discuss the atomic inversion as well as the entropy squeezing and variance squeezing phenomena. We have shown that the existence of the second field coupling parameter reduces the amount of squeezing in all quadratures, while the effect of the detuning parameter would lead to the superstructure phenomenon which becomes more pronounced upon increasing the mean photon numbers, in the states which are taken to be converter states.