Two-photon-driven nonlinear dynamics and entanglement of an atom in a nonuniform cavity

In this paper we study the dynamics in the general case for a Tavis-Cummings atom in a nonuniform cavity. In addition to the dynamical Stark shift, the center-of-mass motion of the atom and the recoil effect are considered in both the weak and the strong cavity-atom coupling regimes. It is shown that the spatial motion of the atom inside the cavity in the resonant case leads to a transition between topologically different solutions. This effect is manifested by a singularity in the interlevel transition spectrum. In the nonresonant case, the spatial motion of the atom leads to a switching of the spin orientation. In both effects, the key factor is the relation between the values of the Stark shift and the cavity-field coupling constant. We also investigate the entanglement of an atom in the cavity with the radiation field. It is shown that the entanglement between the atom and the field, usually quantified in terms of purity, decreases with increasing Stark shift.