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

Abstract

We studied the interaction of a two-level atom with a frequency modulated cavity mode in an ideal optical cavity. The system, described by a Jaynes-Cumming Hamiltonian, gave rise to a set of stiff nonlinear first order equations solved numerically using implicit and semi-implicit numerical algorithms. We explored the evolution of the atomic system using nonlinear dynamics tools, like time series, phase plane, power spectral density, and Poincaré sections plots, for monochromatic and bichromatic modulations of the cavity field. The system showed quasiperiodic and possibly chaotic behavior when the selected monochromatic frequencies, or ratio of the bichromatic frequencies were irrational (incommensurate) numbers. In addition, when the modulated frequencies were overtones of the Rabi frequency of the system, a single dominant frequency emerged for the system.

Quantum Jaynes–Cummings model for a two-level system with effects of parametric time-dependences

“…The interactions between a two-level atom and a quantized single-mode electromagnetic field have attracted much attention in the physics community up until now, thanks to their potential applicability in the state-of-the-art science [1][2][3][4][5][6]. The experiments of such interactions reveal many novel quantum effects, such as the quantum collapses and revivals of atomic inversion [7,8], photon antibunching [9], squeezing of the radiation field [3,10], inversionless light amplification [11], and inducing a controllable transparency [12,13].…”