The full effect of adiabatically varying Hamiltonians on systems prepared in eigenstates of the stationary Hamiltonian often includes geometric Berry's phases. For degenerate systems these effects may result in transitions between distinct degenerate eigenstates that can be described in terms of a non-Abelian gauge potential. I demonstrate the explicit dynamic origin of such transitions between degenerate angular-momentum sublevels in an atom that is subject to collinear electric and magnetic fields that rotate adiabatically. The origin of the effects becomes clear when eigenstates of the total Hamiltonian, which includes the rotating fields, are calculated. The total Hamiltonian removes the degeneracy, and the eigenstates are in some cases linear combinations of the angular-momentum sublevels. Thus a system prepared in a specific sublevel may not remain in that sublevel, and the transition probability is exactly that given by an analysis of the geometric phase.
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 dipole moment over degenerate magnetic sublevels 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 sublevels. Possible applications of our results are discussed.
A method for quantum interferometry and phase control of degenerate Rydberg states has been proposed and realized experimentally. Phase control was carried out by a pulse of a weak dc electric field which caused a Stark splitting of degenerate Rydberg sublevels for a short time. A strong interference dependence of the probability of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ in sodium Rydberg atoms on a phase difference between the Stark sublevels of the
37P3/2 state has been detected. Changes in the probability were measured directly by a pulsed resonant microwave radiation applied after the electric-field pulse. Records of the quantum interference signals and Stark spectra of the microwave transition are presented and discussed. An influence of the laboratory magnetic field has been analyzed.