Pancharatnam Phase of Two-Mode Optical Fields with Kerr Nonlinearity

The Pancharatnam phase when an ideal cavity is filled with a Kerr-like medium and coupling is affected through a nondegenerate Raman two-photon process is studied. A careful investigation is made seeking exact results on 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 Pancharatnam phase contains explicit information about the statistics of the field and atomic coherence, and is also shown that addition of the Kerr medium has an important effect on the properties of this phase. The results show that the effect of the Kerr medium changes the quasiperiod of the Pancharatnam phase evolution. The influence of Stark shift on the atomic inversion and the Pancharatnam phase in both presence and absence of the nonlinear medium is examined. General conclusions reached are illustrated by numerical results.