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Physical Review A

Non-Markovianity of the damped Jaynes-Cummings model with detuning

Jungang Li, Jian Zou, Bin Shao

Published Jun 23, 2010• 84 citations
Publisher

Abstract

The degree of non-Markovian behavior of a damped Jaynes-Cummings model with detuning is investigated. Our attention is focused on the effects of the detuning and the width of the Lorentzian spectral density on the degree of non-Markovian behavior. It is found that an increase of the detuning can make the information exchange between the qubit and the reservoir more rapid, and this leads to an increase in the degree of non-Markovianity for some cases, while an increase of the spectral width always leads to a decrease in the degree of non-Markovianity.

DOI
10.1103/physreva.81.062124

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The degree of non-Markovian behavior of a damped Jaynes-Cummings model with detuning is investigated. Our attention is focused on the effects of the detuning and the width of the Lorentzian spectral density on the degree of non-Markovian behavior. It is found that an increase of the detuning can make the information exchange between the qubit and the reservoir more rapid, and this leads to an increase in the degree of non-Markovianity for some cases, while an increase of the spectral width always leads to a decrease in the degree of non-Markovianity.
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 investigate the influence of phonon degrees of freedom on the qubit dynamics in Jaynes-Cummings (JC) model. A strong qubit-phonon coupling is considered giving rise to Jaynes-Cummings-Holstein (JCH) model. Under anti-adiabatic conditions, we perform a unitary transformation to make the underlying problem tractable through Redfield-type non-Markovian master equation. Analytical expression for the time-dependent coherence is obtained, incorporating both cavity-induced dissipation and phonon-induced dressing effects. The dynamics of JC model is highly non-Markovian for a narrow spectral width and finite detuning. However, a non-zero phonon coupling suppresses these non-Markovian features by effectively reducing the qubit-cavity interaction strength. {It is observed that polaronic dressing effectively supresses the detuning effects. Furthermore, the coherence-based non-Markovianity measure shows an order-of-magnitude suppression in the JCH model, indicating a new dynamical regime, while memory effects extend over a wider range of spectral densities than in the JC model.
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.
Abstract This chapter applies the time-convolutionless projection operator technique to some typical systems featuring strong non-Markovian behaviour. The first example models the decay of a two-level system into a reservoir with arbitrary spectral density. For this problem the expansion of the master equation is carried out to all orders in the system-reservoir coupling. As specific cases the damped Jaynes–Cummings model and the spontaneous decay into a photonic band gap are studied. The model is used to exemplify the breakdown of the expansion in the strong coupling regime, and to illustrate the emergence of completely positive master equations which are not in Lindblad form and involve negative decay rates. The chapter also treats the non-Markovian dynamics in quantum Brownian motion and in the spin-boson model, and illustrates the stochastic unravelling of non-Markovian quantum processes.
We investigate the dynamics of nonclassical correlations including concurrence and local quantum uncertainty in the damped Jaynes–Cummings model with an initial system–reservoir correlation. The dynamics of qubit–reservoir correlation and the influence of non-Markovian effect are studied. Furthermore, we consider the double damped Jaynes–Cummings model consisting of two noninteracting qubits locally coupled to independent reservoirs and explore the properties of both qubit–qubit and reservoir–reservoir correlations. The influences of initial correlation and non-Markovian effect on the dynamics of nonclassical correlations are analyzed. It is found that the dynamics for both qubit–qubit and reservoir–reservoir correlations can be significantly changed by the initial correlation and the non-Markovian effect. Finally, we explore the sudden changes of local quantum uncertainty and find that they are closely related to the initial system–environment entanglement.
The atomic entropy squeezing of the Jaynes-Cummings model driven by classical fields in non-Markovian environment is investigated according to the non-Markovian quantum theory and the entropy squeezing theory. Our attention is focused on the influences of the non-Markovian effects, the Rabi frequencys of classical fields and the detuning on the atomic entropy squeezing. And we explain the atomic entropy squeezing dynamic by the memory effects of the non-Markovian processes. It is found that the atomic entropy squeezing can be maintained for a long time when both the Rabi frequencys of classical fields and the non-Markovian effect are present simultaneously. And we can obtain the optimal squeezing states by choosing appropriate parameters of the Rabi frequency and the detuning of classical field. Our results provide a potential method of generating high-degree squeezed and longtime atomic squeezing states by controlling the atom-field interaction.