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Journal of South China Normal University

PANCHARATNAM PHASE IN DEFORMED JAYNES-CUMMINGS MODEL

Ruisheng Liang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The Pancharatnam phase of deformed Jaynes-Cummings(J-C) model was obtained analytically.The evolution of Pancharatnam phase for deformed Jaynes-Cummings model,was also discussed.The difference between the Pancharatnam phase evolution for deformed J-C model and that of conventional J-C model has been investigated.The results show that the Pancharatnam phase reveals some information of population reversion of an atom and the quantum nature of the cavity field.And the larger is the average photon number,the larger is the difference of Pancharatnam phase evolution between deformed J-C model and conventional J-C model.This exhibits that the evolution of Pancharatnam phase is closely relative to the quantum algebra structure of the system.

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The Pancharatnam phase of deformed Jaynes-Cummings(J-C) model was obtained analytically.The evolution of Pancharatnam phase for deformed Jaynes-Cummings model,was also discussed.The difference between the Pancharatnam phase evolution for deformed J-C model and that of conventional J-C model has been investigated.The results show that the Pancharatnam phase reveals some information of population reversion of an atom and the quantum nature of the cavity field.And the larger is the average photon number,the larger is the difference of Pancharatnam phase evolution between deformed J-C model and conventional J-C model.This exhibits that the evolution of Pancharatnam phase is closely relative to the quantum algebra structure of the system.
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.
Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model.With the the field initially being in three different types of q-deformed coherent states,the quantum collapse and revival effects as well as atomic diploe squeezing are studied for both on-and off-resonant atom-field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures which are absent in the non-deformed Jaynes-Cummings model and the dipole squeezing may be enhanced.
The Pancharatnam phase in simple polariton model is investigated, and the influences of temperature, coupling strength, frequency difference of photon and phonon and average photon number on the evolution dynamics of Pancharatnam phase are also discussed. The results show that the Pancharatnam phase oscillates with time, the oscillating frequency and wave-form vary with time, and the variation increases with the enhancement of temperature, coupling strength and frequency difference of photon and phonon. The system Pancharatnam phase evolutes regularly when the average photon number of coherent light is small, while it becomes more chaotic as the average photon number increases.
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.