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Physics Letters A

Pancharatnam phase for a system of a two-level atom interacting with a quantized field in a cavity

Q. V. Lawande, S. V. Lawande, Amitabh Joshi

Published Jan 1, 1999• 31 citations
Publisher
DOI
10.1016/s0375-9601(98)00882-2

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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.
In this paper we consider a Hamiltonian modelling a pair of two-level atoms within a perfect cavity for the case of a two-photon transition. Under the exact resonance condition and in the presence of both the Stark shift and phase shift an exact solution to the Schrödinger equation is obtained. Employing this solution gives an analytical expression for the temporal evolution of the Pancharatnam phase when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom. Numerical investigations are carried out for the phenomena of collapses and revivals for different Stark shift values, the distance between the two atoms and the phase shift. It has been shown that the Pancharatnam phase is affected by the Stark shift and the distance between the two atoms when a nonlinear two-photon process is involved