© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Atomic and Molecular Physics

Microscopic versusphenomenological master equations for Jaynes-Cummings model with the cavity losses

Xiao Wang

Published Jan 1, 2013• 0 citations

Abstract

Microscopic and phenomenological Microscopic master equations have been applied to Jaynes-Cummings model with the cavity losses when the initial state of composite system(atom+cavity) is Bell state or atomic excitation state and the field state is vacuum.The differences of the two kinds of master equations have been analyzed in different coupling regimes.We find that in strong coupling regime,the increase of the population of atomics ground state is linear using the microscopic master equation,but it is non-linear by the phenomenological master equation under large coupling constants.In small coupling constants the population of atomic ground state is similar to the situations in large coupling constants.Although the ground-state populations in the two equations increase rapidly in weak coupling region,this result by phenomenological master equation increases faster than that by microscopic master equation.The conclusion may be useful for cavity quantum electrodynamics(QED) in losses cavity to provide guidance for the realization of logical gate.

Related papers

Microscopic derivation of the Jaynes-Cummings model with cavity losses

M. Scala, Benedetto Militello, ANTONINO MESSINA +2 more

In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.

arXiv:quant-ph/0610140•Physical Review A•Jan 22, 2007•133 citations

Microscopic approach to field dissipation in the Jaynes–Cummings model

Carlos A. González-Gutiérrez, D Solís-Valles, B. M. Rodríguez-Lara

Abstract We use the microscopic derivation of the Jaynes–Cummings model master equation under field losses to study the dynamics of initial field-qubit states in the single-excitation manifold and beyond. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate of the system using measures like field-qubit purity and concurrence for the case of one-excitation, and for initial Fock states for more excitations. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the standard phenomenological approach.

arXiv:1707.07056•Journal of Physics A Mathematical and Theoretical•Oct 16, 2017•6 citations

Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation

M Scala, B Militello, A Messina +3 more

A microscopic derivation of the master equation for the Jaynes–Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows us to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis (Scala et al 2007 Phys. Rev. A 75 013811 ), where a microscopic derivation was given in the framework of the rotating wave approximation.

arXiv:0709.1614•Journal of Physics A Mathematical and Theoretical•Nov 14, 2007•58 citations

Nonequilibrium dynamics of the dispersive Jaynes–Cummings model by a non-Markovian quantum master equation

Masashi Ban

Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.

Journal of Physics A Mathematical and Theoretical•Jul 16, 2010•7 citations

Analytic approach to dynamics of the resonant and off-resonant Jaynes-Cummings systems with cavity losses

Soshun Ozaki, Hiromichi Nakazato

An analytic approach to investigate the zero-temperature time evolution of the Jaynes-Cummings system with cavity losses is developed. With realistic coupling between the cavity and the environment assumed, a simple master equation is derived, leading to the explicit analytic solution for the resonant case. This solution is suitable for analyses not only on single-excitation states but also on many-excitation states, which enables us to investigate the photon coherent state and to observe sharp collapses and revivals under dissipation. For the off-resonant case, on the other hand, the present study presents an analytic, systematic method instead. We examine the small and large detuning limits and discuss the condition where the widely used phenomenological treatment is justified. Explicit evaluations of the time evolutions for various initial states with finite detuning are also presented.

arXiv:2103.08257•Physical Review A•May 28, 2021•7 citations

Cavity losses for the dissipative Jaynes-Cummings Hamiltonian beyond Rotating Wave Approximation

M. Scala, Benedetto Militello, ANTONINO MESSINA +3 more

Abstract. A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. et al. 2007 Phys. Rev. A 75, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation. PACS numbers: 42.50.Lc, 03.65.Yz, 42.50.PqCavity losses for the dissipative Jaynes-Cummings Hamiltonian beyond RWA 2

•Nov 21, 2012•38 citations

Microscopic and phenomenological Microscopic master equations have been applied to Jaynes-Cummings model with the cavity losses when the initial state of composite system(atom+cavity) is Bell state or atomic excitation state and the field state is vacuum.The differences of the two kinds of master equations have been analyzed in different coupling regimes.We find that in strong coupling regime,the increase of the population of atomics ground state is linear using the microscopic master equation,but it is non-linear by the phenomenological master equation under large coupling constants.In small coupling constants the population of atomic ground state is similar to the situations in large coupling constants.Although the ground-state populations in the two equations increase rapidly in weak coupling region,this result by phenomenological master equation increases faster than that by microscopic master equation.The conclusion may be useful for cavity quantum electrodynamics(QED) in losses cavity to provide guidance for the realization of logical gate.

Abstract We use the microscopic derivation of the Jaynes–Cummings model master equation under field losses to study the dynamics of initial field-qubit states in the single-excitation manifold and beyond. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate of the system using measures like field-qubit purity and concurrence for the case of one-excitation, and for initial Fock states for more excitations. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the standard phenomenological approach.

A microscopic derivation of the master equation for the Jaynes–Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows us to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis (Scala et al 2007 Phys. Rev. A 75 013811 ), where a microscopic derivation was given in the framework of the rotating wave approximation.

Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.

An analytic approach to investigate the zero-temperature time evolution of the Jaynes-Cummings system with cavity losses is developed. With realistic coupling between the cavity and the environment assumed, a simple master equation is derived, leading to the explicit analytic solution for the resonant case. This solution is suitable for analyses not only on single-excitation states but also on many-excitation states, which enables us to investigate the photon coherent state and to observe sharp collapses and revivals under dissipation. For the off-resonant case, on the other hand, the present study presents an analytic, systematic method instead. We examine the small and large detuning limits and discuss the condition where the widely used phenomenological treatment is justified. Explicit evaluations of the time evolutions for various initial states with finite detuning are also presented.

Abstract. A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. et al. 2007 Phys. Rev. A 75, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation. PACS numbers: 42.50.Lc, 03.65.Yz, 42.50.PqCavity losses for the dissipative Jaynes-Cummings Hamiltonian beyond RWA 2