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 degenerate two-photon process is studied. The exact results are employed to perform a careful investigation of the temporal evolution of atomic inversion and Pancharatnam phase. We invoke the mathematical notion of maximum variation of a function to construct a measure for Pancharatnam phase fluctuations. It is shown that the Pancharatnam phase explicity contains information about 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 Pancharatnam phase evolution. The general conclusions reached are illustrated by numerical results.