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Optical Review

Pancharatnam Phase of Two-Mode Optical Fields with Kerr Nonlinearity

Mahmoud Abdel‐Aty, S. Abdel‐Khalek, A.‐S. F. Obada

Published Nov 1, 2000• 37 citations
Publisher
DOI
10.1007/s10043-000-0499-6

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Canadian Journal of Physics•Apr 1, 2009•9 citations
The Pancharatnam phase properties of two coupling-atoms and a single-mode squeezed state light field in nonlinear Kerr medium were studied.Selecting proper initial conditions to solve the Schrodinger equation by the rotating wave approximation,and the Pancharatnam phase specific form was obtained.The results show that the two coupling-atoms' initial states are in any form,the Pancharatnam phase frequency increases when the interaction strength between atoms and light field,and the dipole-dipole coupling strength between two atoms or the Kerr medium's nonlinearity increases.The Pancharatnam phase evolution shows obvious trend of oscillating and rising(or fall) when the initial state is that two atoms are both in the excited states.As the growth of the Kerr medium'nonlinearity,the Pancharatnam phase evolution becomes disordered when the initial state is that just one atom is in excited state.
The Pancharatnam phase of a Tavis-Cummings model with the coherent state in Kerr medium is investigated theoretically and numerically. An exact expression of the Pancharatnam phase under this general system is obtained. The numerical results show that the dipole-dipole coupling strength between two atoms can change the quasi-period of the Pancharatnam phase evolution,and it is also proved that the Pancharatnam phase contains the information of atoms and the field. In the nonlinear interaction regime, the nonlinearity can cause the chaotic behavior of the Pancharatnam phase.
The formalism of path integral is used to treat the influence of Stark shift on the atomic population inversion (API) and Pancharatnam phase in the Jaynes–Cummings model with a nonlinear Kerr cavity. The propagators are given explicitly as perturbation series. In the case of a quantized wave interacting with a two-level system, these are summed up exactly, and the corresponding Pancharatnam phase as well as atomic population inversion, and energy spectrum with corresponding wave functions are deduced.