Entanglement properties of an ultracold atom interacting with a cavity quantized electromagnetic field

We study the temporal evolution of the properties of a two-level atom coupled to a single-mode cavity field without dissipation with its center-of-mass motion quantized in one dimension. It is shown that, starting with a separable state, genuine tripartite entangled states can be generated under resonance conditions of the light frequency and atom transition frequency in the cold regime. The onset of Rabi oscillations is analyzed and explicit predictions for properties like emission probability and dispersions for the center-of-mass position and momenta are given for resonance and detuned conditions. Transmission-resonance effects on entanglement and other properties are also analyzed. Comparisons with the semiclassical adiabatic approximation predictions are also made.