Tunneling and Traversal of Ultra-cold Atoms through Vacuum Induced Potentials

We examine the passage of ultra-cold two-level atoms through the potential produced by the vacuum of the cavity field. The peak of the transmitted wave packet generally occurs at the instant given by the expression for phase time even if that instant is earlier than the instant at which incident wave packet's peak enters the cavity and thus the phase time can be considered as the appropriate measure of the time required for the atom to traverse the cavity. We show that the phase tunneling time for ultra-cold atoms could be both super - and sub - classical time and we show how this behaviour can be understood in terms of the momentum dependence of the phase of transmission amplitude. The passage of the atom through the cavity is unique as it involves a coherent addition of the transition amplitudes corresponding to both barrier and well. New features such as the splitting of the wave packet arise from the entanglement between the center of mass motion and the electronic as well as field states in the cavity.