Continuous control of the coupling constant in an atom-cavity system by using elliptic polarization and magnetic sublevels

Atom-cavity coupling constant is a key parameter in cavity quantum electrodynamics for describing the interaction between an atom and a quantized electromagnetic field in a cavity. This paper reports a novel way to tune the coupling constant continuously by inducing an averaging of the atomic dipóle moment over degenerate magnetic subleveis with elliptic polarization of the cavity field. We present an analytic solution of the stationary-state density matrix for this system with consideration of F → F + 1 hyperfine transition under a weak excitation condition. We rigorously show that the stationary-state emission spectra of this system can be approximated by that of a non-degenerate two-level atom with an effective coupling constant as a function of the elliptic angle of the cavity field only. A precise condition for this approximation is derived and its physical meaning is interpreted in terms of a population-averaged transition strength and its variance. Our results can be used to control the coupling constant in cavity quantum electrodynamics experiments with a degenerate two-level atom with magnetic subleveis. Possible applications of our results are discussed.