Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Canadian Journal of Physics

Pancharatnam phase for the generalized Jaynes–Cummings model with a nonlinear Kerr cavity

Mekki Aouachria, L. Chétouani

Published Apr 1, 2009• 9 citations
Publisher

Abstract

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.

DOI
10.1139/p08-117

Related papers

Path integral for the generalized Jaynes-Cummings model

Tahar Boudjedaa, Abdelhafid Bounames, Khireddine Nouicer +2 more

We use the coherent state path integral and a fermion model for the spin to solve a non-linear bosonic generalization of the Jaynes-Cummings model. The propagators are given explicitly as perturbation series. These are summed up exactly for special cases and the corresponding atomic population inversion as well as energy spectrum and wave functions are deduced.

Physica Scripta•Sep 1, 1996•14 citations

Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

Anita Bandyopadhyay, Gautam Gangopadhyay

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.

Journal of Modern Optics•Mar 1, 1996•11 citations

Entropy squeezing and atomic inversion in the k -photon Jaynes—Cummings model in the presence of the Stark shift and a Kerr medium: A full nonlinear approach

H R Baghshahi, M K Tavassoly, A Behjat

The interaction between a two-level atom and a single-mode field in the k -photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f -deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).

arXiv:1408.2975•Chinese Physics B•Jul 1, 2014•55 citations

Exact solution of generalized Tavis - Cummings models in quantum optics

N. M. Bogoliubov, R. Bullough, JUSSI TIMONEN

Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogeneous ordinary differential equation of second order. Generalization of the method to the case of several cavity modes is indicated.

Journal of Physics A Mathematical and General•Oct 7, 1996•108 citations

The Pancharatnam phase of a two-level atom in the presence of another two-level atom in a cavity

Mahmoud Abdel‐Aty

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

Journal of Optics B Quantum and Semiclassical Optics•Jul 2, 2003•19 citations

Pancharatnam Phase in a Tavis-Cummings Model with Nonlinearity

廖浩祥 LIAO Hao-xiang, 王发强 WANG Fa-qiang, 梁瑞生 LIANG Rui-sheng

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.

ACTA PHOTONICA SINICA•Jan 1, 2010•0 citations
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.
An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.
The interaction between a two-level atom and a single-mode field in the k -photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f -deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).
Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogeneous ordinary differential equation of second order. Generalization of the method to the case of several cavity modes is indicated.
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
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.