  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.
