Pancharatnam phase of two-mode optical fields with Kerr nonlinearity

The Pancharatnam phase when an ideal cavity is filled with a I(err-like med ium and coupling is affected through a nondegenerate Raman two-photon proce ss is studied. A careful investigation is made seeking exact results on the temporal evolution of atomic inversion and Pancharatnam phase. We invoke t he mathematical notion of maximum variation of a function to construct a me asure for Pancharatnam phase fluctuations. It is shown that Pancharatnam ph ase contains explicit information about the statistics of the held and atom ic coherence, and is also shown that addition of the Kerr medium has an imp ortant effect on the properties of this phase. The results show that the ef fect of the Kerr medium changes the quasiperiod of the Pancharatnam phase e volution. The influence of Stark shift on the atomic inversion and the Panc haratnam phase in both presence and absence of the nonlinear medium is exam ined. General conclusions reached are illustrated by numerical results.