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

Journal of Optics B Quantum and Semiclassical Optics

A joint Wigner function of an atom-field system with dissipation

L. Sanz, K. Furuya

Published Apr 5, 2002• 5 citations
Publisher

Abstract

We found analytically the exact joint Wigner function (WF) of an atom-field system described by the Jaynes-Cummings model in the dispersive limit for a given initial state. Using the solution of a master equation with a dissipative term calculated by Peixoto de Faria and Nemes (Peixoto de Faria J G and Nemes M C 1999 Phys. Rev. A 59 3918) and a general expression for the joint WF proposed by Czirják and Benedict (Czirják A and Benedict M G 1996 Quantum Semiclass. Opt. 8 975), we obtained the exact reduced atom and field WFs and analysed their time evolution. Our results show that, at the maximum entanglement times, the atom tends to a statistical mixture state represented by a spherical polar plot. Also, the atomic WF shows how fast the negative-valued part disappears as a function of dissipation constant and the strength of the field coherent state.

DOI
10.1088/1464-4266/4/3/373

Related papers

Dispersive limit of the dissipative Jaynes–Cummings model with a squeezed reservoir

V. V. Dodonov, Wagner Duarte José, Salomon Sylvain Mizrahi

We consider the dynamics of an atom–field system in a cavity described by means of the Jaynes–Cummings model in the dispersive limit, assuming that the electromagnetic field is interacting with a squeezed, or phase-sensitive, reservoir. After obtaining the solution of the master equation in terms of Wigner functions, we do an analysis of the system evolution and its asymptotical behaviour in terms of the so-called Mandel Q parameter and the linear entropies of the total system and the reduced system, associated with field and atom.

Journal of Optics B Quantum and Semiclassical Optics•Oct 16, 2003•11 citations

Función de Wigner y Decoherencia Cuántica para Sistemas Átomo-Campo en Cavidades QED

Juan Pablo Cuartas, Herbert Vinck Posada, Boris A. Rodríguez

ABSTRACT: The processes of quantum decoherence in QED cavities have been extensively studied in the last decade, both experimentally by Haroche, Raimond et. al., as theoretically by Nemes, Davidovich et. to the. We present here the dynamics of the Wigner function for a system consisting of a two-level atom and a cavity in a dissipative environment, using a numerical integration scheme that allows us to consider initial Squeezed and Schrodinger's Cat States. The interaction between the atom and the single-mode field is considered by a dispersive model, that is, the interaction in the Hamiltonian of Jaynes-Cummings appears as a small disturbance. The interest is focused both on the quantum characteristics of the dispersive approach (preparation of mesoscopic states) and on the aspects that characterize dynamics and dissipation. In particular, the gradual loss of quantum coherence is observed through the use of the Wigner function, where the disappearance of the interference regions of the initial quantum states is evidenced.

Revista de la Sociedad Colombiana de Física•Jan 1, 2009•0 citations

Output entanglement fromSU(1, 1) coherent states under nonlinear dissipation in the dispersive limit

A.‐S. F. Obada, H. A. Hessian, A.‐B. A. Mohamed

An analytical solution is found for the master equation of a system described by a nonlinear Jaynes–Cummings model, in the presence of nonlinear quantum dissipation at zero temperature in the large detuning approximation. We study the influence of nonlinear quantum dissipation on the output entanglement dynamics of the atom–field system, considering the field to be initially in SU (1, 1) coherent states. It is found that in the presence of the nonlinear quantum dissipation, the amplitude of the output entanglement between the field and the atom decreases with time, however the entanglement between the field–atom system and the environment increases with time.

Journal of Physics A Mathematical and Theoretical•Dec 10, 2009•11 citations

Coherence Loss of Two-Photon Jaynes–Cummings Model in Dispersive Approximation

Zhou Ling, Yanqing Guo, He‐Shan Song +1 more

Completely solving the dissipative dynamics of nonlinear Jaynes–Cumming model is a very difficult task. In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain the density operator of the system (field +atom). The coherence losses of the system and of the atom are investigated when two-photon process is involved. We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.

Communications in Theoretical Physics•Jan 15, 2004•1 citation

Coherence Loss of Two-Photon Jaynes-Cummings Model in Dispersive Approximation

Yan Guo

Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task. In our recent work(Phys.Lett.A284(2001)156),we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM.In the present paper,employing the perturbative expansion of master equation,we obtain the density operator of the system(field+atom).The coherence losses of the system and of the atom are investigated when two-photon process is involved.We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.

理论物理通讯：英文版•Jan 1, 2004•0 citations

Coherence Loss of Two-Photon Jaynes-Cummings Model in Dispersive Approximation

ZHOULing, GUOYan-Qing, SONGHe-Shan +1 more

Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task.In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamicsof the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain thedensity operator of the system (field +atom). The coherence losses of the system and of the atom are investigated whentwo-photon process is involved. We also study the effect of different atomic initial states and the influence of the fieldamplitude on the atomic coherence loss.

理论物理通讯：英文版•Jan 1, 2004•0 citations
We found analytically the exact joint Wigner function (WF) of an atom-field system described by the Jaynes-Cummings model in the dispersive limit for a given initial state. Using the solution of a master equation with a dissipative term calculated by Peixoto de Faria and Nemes (Peixoto de Faria J G and Nemes M C 1999 Phys. Rev. A 59 3918) and a general expression for the joint WF proposed by Czirják and Benedict (Czirják A and Benedict M G 1996 Quantum Semiclass. Opt. 8 975), we obtained the exact reduced atom and field WFs and analysed their time evolution. Our results show that, at the maximum entanglement times, the atom tends to a statistical mixture state represented by a spherical polar plot. Also, the atomic WF shows how fast the negative-valued part disappears as a function of dissipation constant and the strength of the field coherent state.
We consider the dynamics of an atom–field system in a cavity described by means of the Jaynes–Cummings model in the dispersive limit, assuming that the electromagnetic field is interacting with a squeezed, or phase-sensitive, reservoir. After obtaining the solution of the master equation in terms of Wigner functions, we do an analysis of the system evolution and its asymptotical behaviour in terms of the so-called Mandel Q parameter and the linear entropies of the total system and the reduced system, associated with field and atom.
ABSTRACT: The processes of quantum decoherence in QED cavities have been extensively studied in the last decade, both experimentally by Haroche, Raimond et. al., as theoretically by Nemes, Davidovich et. to the. We present here the dynamics of the Wigner function for a system consisting of a two-level atom and a cavity in a dissipative environment, using a numerical integration scheme that allows us to consider initial Squeezed and Schrodinger's Cat States. The interaction between the atom and the single-mode field is considered by a dispersive model, that is, the interaction in the Hamiltonian of Jaynes-Cummings appears as a small disturbance. The interest is focused both on the quantum characteristics of the dispersive approach (preparation of mesoscopic states) and on the aspects that characterize dynamics and dissipation. In particular, the gradual loss of quantum coherence is observed through the use of the Wigner function, where the disappearance of the interference regions of the initial quantum states is evidenced.
An analytical solution is found for the master equation of a system described by a nonlinear Jaynes–Cummings model, in the presence of nonlinear quantum dissipation at zero temperature in the large detuning approximation. We study the influence of nonlinear quantum dissipation on the output entanglement dynamics of the atom–field system, considering the field to be initially in SU (1, 1) coherent states. It is found that in the presence of the nonlinear quantum dissipation, the amplitude of the output entanglement between the field and the atom decreases with time, however the entanglement between the field–atom system and the environment increases with time.
Completely solving the dissipative dynamics of nonlinear Jaynes–Cumming model is a very difficult task. In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain the density operator of the system (field +atom). The coherence losses of the system and of the atom are investigated when two-photon process is involved. We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.
Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task. In our recent work(Phys.Lett.A284(2001)156),we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM.In the present paper,employing the perturbative expansion of master equation,we obtain the density operator of the system(field+atom).The coherence losses of the system and of the atom are investigated when two-photon process is involved.We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.
Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task.In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamicsof the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain thedensity operator of the system (field +atom). The coherence losses of the system and of the atom are investigated whentwo-photon process is involved. We also study the effect of different atomic initial states and the influence of the fieldamplitude on the atomic coherence loss.