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Acta Physica Sinica

Comparison of entanglement decay between Bell-like states under different environmental models

Wei Han, Cui Wen-Kai, Zhang Ying-Jie, Yun‐Jie Xia

Published Jan 1, 2012• 5 citations
Publisher

Abstract

Establishing three different environment models (i.e., single reservoir model, common reservoir model and independent reservoir model), we investigate the evolutional characteristic of the entangled system initially in Bell-like state by the pseudomode method. Through comparing the entanglement decays under the three different environment models, we find that the entangled Bell-like state cos θ |ee> + sin θ |gg> will be kept in the single reservoir model for a time longer than in the other two models. However, the entanglement decay behavior of Bell-like state cos θ |eg> + sin θ |ge> is dependent on the specific environment model. Meanwhile, the comparison of entanglement decay between the above two Bell-like states at the same environment models is performed.

DOI
10.7498/aps.61.230302

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Establishing three different environment models (i.e., single reservoir model, common reservoir model and independent reservoir model), we investigate the evolutional characteristic of the entangled system initially in Bell-like state by the pseudomode method. Through comparing the entanglement decays under the three different environment models, we find that the entangled Bell-like state cos θ |ee> + sin θ |gg> will be kept in the single reservoir model for a time longer than in the other two models. However, the entanglement decay behavior of Bell-like state cos θ |eg> + sin θ |ge> is dependent on the specific environment model. Meanwhile, the comparison of entanglement decay between the above two Bell-like states at the same environment models is performed.
We investigate the roles of different qubit—environment decoherence models on the entanglement trapping of two qubits. By considering three environmental models (the single photonic band gap model, the common photonic band gap model, and the two independent photonic band gaps model), we note that the final values of entanglement trapping are determined by these different models. We also give the conditions of obtaining the larger entanglement trapping by comparing two-qubit entanglement dynamics in different decoherence models. Moreover, the comparison of entanglement trapping between two Bell-like states in the same decoherence model are also carried out.
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservoir to the cavity modes depend crucially on the matching of the initial correlations to that contained in the squeezed reservoir. In particular, it is found that initially entangled modes with correlations different from the reservoir correlations prevent the transfer of the correlations from the squeezed field to the modes. In addition, we find that the transient entanglement exhibits several features unique to quantum nature of squeezing. In particular, we show that in the case of separate squeezed reservoirs a variation of the decay time of the initial entanglement with the squeezing phase is unique to quantum squeezing. In the case of a common reservoir a recurrence of entanglement occurs and we find that this feature also results from the reservoir correlations unique to quantum squeezing. There is no revival of entanglement when the modes interact with a classically squeezed field.
In this paper,the dynamics evolution and transfer of the atomic concurrence and the cavities concurrence are investigated in the coupled-cavity model.The results show that the coupling coefficient between two cavities plays different roles on evolutional behaviors for the initial entanglement in the different Bell states.In the case of the first Bell state cosθ|e,e〉+sinθ|g,g〉,the coupling coefficient between two cavities not only can prolong the time of entanglement death,but also can preserve the initial atomic entanglement.While for the case of the other Bell state cosθ|e,g〉+sinθ|g,e〉,the coupling coefficient between two cavities only can give a protection for the initial atomic entanglement.
Dynamics of entangled states of two independent single-mode cavities in a correlated (squeezed) reservoir are investigated in the context of matching the correlations contained in the entangled states to those contained in the reservoir. We illustrate our considerations by examining the time evolution of entanglement of initial single and double excitation NOON and EPR states, and a comparison is made of when each cavity is coupled to its own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservoir to the cavity modes depend crucially on the matching of the initial correlations to those contained in the squeezed reservoir. In particular, it is found that initially entangled modes with correlations different from the reservoir correlations prevent the transfer of the correlations from the squeezed field to the modes. In addition, we find that the transient entanglement exhibits several features unique to the quantum nature of squeezing. In particular, we show that in the case of separate squeezed reservoirs the initial entanglement disappears at a finite time, which for the so-called classically squeezed field remains almost the same as in the case of a thermal field. In the case of a common reservoir a recurrence of entanglement occurs and we find that this feature also results from the reservoir correlations unique to quantum correlations. There is no revival of the entanglement when the modes interact with a classically correlated field.
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.