Pancharatnam phase of an effective two-level atom in a Kerr-like medium

The influence of Stark shift on the Pancharatnam phase when an ideal cavity is filled with a Kerr-like medium and coupling is affected through a degen erate two-photon process is studied. The exact results are employed to perf orm a careful investigation of the temporal evolution of atomic inversion a nd Pancharatnam phase. We invoke the mathematical notion of maximum variati on of a function to construct a measure for Pancharatnam phase fluctuations . It is shown that the Pancharatnam phase explicity contains information ab out the statistics of the field and atomic coherence. It is shown that the addition of the Kerr medium and the Stark shift has an important effect on the properties of the Pancharatnam phase. The results show that, the effect of the Kerr medium and the Stark shift changes the quasiperiod of the Panc haratnam phase evolution. The general conclusions reached are illustrated b y numerical results.