Quantum Mechanics of Two-Field Parametric Frequency Converter Interacting with a Single Atom

In this communication we deal with a new model Hamiltonian representing the interaction between a two-level atom and two electromagnetic field modes in a cavity. The interaction between the modes has been taken into account and considered to be of a parametric frequency converter type. The model can be regarded as a generalization of two different systems: the Jaynes–Cummings model (atom–field interaction) and the two-mode frequency converter model (field–field interaction). Under a certain condition an exact solution for the equations of motion in the Heisenberg picture is given. The wavefunction in the Schrödinger picture is also constructed and used to discuss some statistical properties related to the model. We assume that the fields are initially in coherent states. We discuss atomic inversion, photon number distribution, squeezing and other phenomena. We show in all cases that the system is very sensitive to any variation in the mean photon numbers.