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Chinese Physics Letters

Quantum Entropy Controlling in the Damping Jaynes–Cummings Model

Jia Fei, Xie Shuang-Yuan, Yang Ya-Ping

Published Jan 1, 2010• 7 citations
Publisher

Abstract

The quantum entropy of the damping Jaynes–Cummings model is investigated in different decay coefficients under detuning conditions. The results indicate that the larger the decay coefficient is, the more quickly the entropy decays. The detuning of the atom and field frequencies reduce the entanglement maximum in short time regions, but delays the damping process of the entanglement. The sine modulation enhances the entanglement in short time regions.

DOI
10.1088/0256-307x/27/1/014212

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The quantum entropy of the damping Jaynes–Cummings model is investigated in different decay coefficients under detuning conditions. The results indicate that the larger the decay coefficient is, the more quickly the entropy decays. The detuning of the atom and field frequencies reduce the entanglement maximum in short time regions, but delays the damping process of the entanglement. The sine modulation enhances the entanglement in short time regions.
Employing projection methods from kinetic theory, we study the non-Markovian quantum evolution of a two-level atom that is coupled to a single mode of the electromagnetic field. The interaction between the atom and field mode is described by the damped Jaynes–Cummings model. The general case is considered, in which dissipation is generated by both a photonic and an atomic reservoir of finite temperature. Only one special choice is made. The frequencies of the atom and field mode are in the same ratio as the temperatures of the atomic and the photonic reservoirs. Making use of Laplace transformation, we show that the atomic density matrix evolves to the state of maximum von Neumann entropy if the time, the cube of the initial electromagnetic energy density, the inverse of the photonic damping parameter and the inverse of the atomic damping parameter tend to infinity equally fast. We propose a large class of states from which the full density operator for the atom and field may start. This class includes entangled states. Expansion of the time-dependent exponential of the Laplace backtransform enables us to derive the limit of maximum entropy directly, without explicit evaluation of the atomic density matrix. We interchange limits and sums without proof, so our derivation is not entirely rigorous. Next, we remove the photonic reservoir. Then the damping process gets a sequential character. The field mode is assumed to start from a photon-number state. For the special choice of zero temperature and detuning we verify that the limit of maximum entropy survives the qualitative modification of the model. The only consequence is a slightly different scaling between the parameters that become large. Finally, we argue that our case study could be of value in finding out to what extent quantum dissipative processes obey the general principles of thermodynamics.
The time evolution of the field quantum entropy in the system of a multi-mode coherent field interacting with a two-level atom through the non-degenerate multi-photon process is investigated using the Von Neumann reduced entropy, the analytical expression of the multimode field entropy including the frequency detuning is obtained. The numerical results for the three-mode field interacting with the atom are presented. The influence of the frequency detuning on the field quantum entropy is discussed. It is found that the frequency detuning has nearly no effect on the entanglement between the three-mode coherent field and the two-level atom when the field and the atom are near resonance, but the time evolution of the field quantum entropy is strongly dependent on the values of the frequency detuning when the field and the atom are far from resonance, especially when the frequency detuning is large enough, the field and the atom are nearly always in entangled states.
In this paper, we analytically solve the master equation for Jaynes–Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model. The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.
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.
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.