Cavity quantum electrodynamics of a two-level atom with modulated fields

We present a numerical study of the interaction of a two-level atom with a frequency-modulated cavity mode described by the Jaynes-Cummings Hamiltonian. In particular, we explore how the population of the atomic levels changes for monochromatic and bichromatic modulations of the cavity field. The primary goal is to find sets of boundary conditions for which the evolution of the system exhibits nonlinear dynamic behavior, by solving the equations of motion of the atomic system using embedded and semi-implicit numerical algorithms. We find that the system shows quasiperiodicity when the monochromatic frequencies or ratio of the bichromatic frequencies of the field are irrational (incommensurate) numbers. In addition, when the modulated frequencies are overtones of the Rabi frequency a nearly single dominant frequency becomes apparent for the evolution of the atomic level population of the system. (C) 2012 American Association of Physics Teachers. [http://dx.doi.org/10.1119/1.3703016]