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Journal of Physics A Mathematical and Theoretical

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

Masashi Ban

Published Jul 16, 2010• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1751-8113/43/33/335305

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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.
Time-evolution of the dispersive Jaynes–Cummings model interacting with a bosonic reservoir is considered in the presence of an initial correlation between the cavity field and reservoir. When there is at most one excitation in the whole system, the exact time-evolution can be obtained. The effects of the initial correlation on the decoherence of the two-level system and cavity field are investigated. Furthermore, the validity of the time-convolutionless quantum master equation in the second-order approximation with respect to the system-reservoir interaction is examined by means of the exact solution.
We study two extensions to the Jaynes Cummings model described by Markovian master equations with Lindblad operators causing either dephasing or photon losses solely involving the cavity mode. We treat the two-level atom as the central system under investigation, while the mode of the cavity plays the role of a near environment coupled via the Lindblad operators to an imagined far environment. We show that increasing the dephasing or damping parameter of the cavity systematically slows the decoherence of the atom. The exact solvability allows us to determine the relation to the quantum Zeno effect and the perturbative regime.
For a two-level atom in a lossy cavity, a scheme to manipulate the non-Markovian speedup dynamics has been proposed in the controllable environment (the lossy cavity field). We mainly focus on the effects of the qubit–cavity detuning Δ and the qubit–cavity coupling strength κ on the non-Markovian speedup evolution of an open system. By controlling the environment, i.e., tuning Δ and κ , two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved. Furthermore, it is clearly found that increasing the coupling strength κ or detuning Δ in some cases can make the environmental non-Markovianity stronger and hence can lead to faster evolution of the open system.
We study the effect of phase damping in the two-mode Jaynes–Cummings model (JCM) using a master equation describing phase damping under the Markovian approximation. An analytic solution of the master equation for the nondegenerate bimodal multiquanta JCM with phase damping is obtained. We show that phase damping has a less detrimental effect on nonclassical properties of the field than energy damping. In contrast to energy damping the strong nonclassical coherences of a Schrödinger's cat superposition state of two well separated coherent states decay with a similar time constant, independent of the separation of the two states.
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.