Dynamics of entanglement protection of two qubits using a driven laser field and detunings:Independent and common,Markovian and/or non-Markovian regimes

Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies.In this regard,we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent(Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field.Then,we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure.It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency,the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies(central detuning) in both non-Markovian and Markovian reservoirs.While the central detuning has a constructive role,the detuning between the qubit and the classical field(laser detuning) affects negatively on the entanglement protection.The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir.We demonstrate that,in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.     

Environmental Effects on Two-Qubit Correlation in the Dispersive Jaynes-Cummings Model

Total, classical and quantum correlations as well as entanglement are studied for a two-qubit system, where each qubit is placed in a micro cavity described by the dispersive Jaynes-Cummings model. Not only the loss of cavity photons but also the effect of the qubit-photon interaction on the loss is taken into account. The two-qubit system is initially prepared in a Bell diagonal state with a single mixing parameter and the cavity photon is either in a superposition of vacuum and single-photon states or in a weak coherent state. It is shown that more correlation of the two qubits can survive as an initial value of the cavity photon number is smaller. There is a threshold value of the cavity photon number, below which the stationary state becomes inseparable. Furthermore it is found that the external environment which causes the cavity loss has two effects; one brings about the decay of the correlations and the other suppresses the decay.     

Entanglement dynamics of two interacting qubits under the influence of local dissipation

We investigate the dynamics of entanglement given by the concurrence of a two-qubit system in the non-Markovian setting. A quantum master equation is derived, which is solved in the eigenbasis of the system Hamiltonian for X-type initial states. A closed formula for time evolution of concurrence is presented for a pure state. It is shown that under the influence of dissipation non-zero entanglement is created in unentangled two-qubit states which decay in the same way as pure entangled states. We also show that under real circumstances, the decay rate of concurrence is strongly modified by the non-Markovianity of the evolution.     

耗散腔中双原子与光场的纠缠演化特性

采用全量子理论方法,研究了处于耗散腔中的双原子与单模相干光场相互作用系统,分析了双原子与光场之间以及两原子之间的纠缠演化特性,讨论了腔场的衰减以及原子与光场间的失谐量对双原子与光场之间以及两原子之间纠缠演化特性的影响.结果表明,当腔场存在损耗时,原子与光场之间可出现纠缠,但在长时极限下,纠缠逐渐消灭|而失谐量对原子与光场间的纠缠存在着显著影响|初始处于最大纠缠的两原子之间的纠缠,由于光场的衰变而逐渐减弱,但原子-光场之间的失谐可抑制这一衰减.     

Entanglement dynamics and decoherence of an atom coupled to a dissipative cavity field

In this paper, we investigate the entanglement dynamics anddecoherence in the interacting system of a strongly driventwo-level atom and a single mode vacuum field in the presence ofdissipation for the cavity field. Starting with an initial productstate with the atom in a general pure state and the field in avacuum state, we show that the final density matrix is supportedon \({\mathbb C}^2\otimes{\mathbb C}^2\) space, and therefore, theconcurrence can be used as a measure of entanglement between theatom and the field. The influences of the cavity decay on thequantum entanglement of the system are also discussed. We alsoexamine the Bell-CHSH violation between the atom and the field andshow that there are entangled states for which the Bell-BCSHinequality is not violated. Using the above system as a quantumchannel, we also investigate the quantum teleportation of ageneric qubit state and also a two-qubit entangled state, and showthat in both cases the atom-field entangled state can be useful toteleport an unknown state with fidelity better than any classicalchannel.     

Two-Qubit Local Fisher Information Correlation beyond Entanglement in a Nonlinear Generalized Cavity with an Intrinsic Decoherence

In this paper, we study a Hamiltonian system constituted by two coupled two-level atoms (qubits) interacting with a nonlinear generalized cavity field. The nonclassical two-qubit correlation dynamics are investigated using Bures distance entanglement and local quantum Fisher information under the influences of intrinsic decoherence and qubit–qubit interaction. The effects of the superposition of two identical generalized coherent states and the initial coherent field intensity on the generated two-qubit correlations are investigated. Entanglement of sudden death and sudden birth of the Bures distance entanglement as well as the sudden changes in local Fisher information are observed. We show that the robustness, against decoherence, of the generated two-qubit correlations can be controlled by qubit–qubit coupling and the initial coherent cavity states.     

耗散腔场中两个∧型原子的纠缠特性

利用超算符方法求解幅值损耗腔中两个∧型三能级原子与相干光场相互作用系统的主方程,并利用量子条件熵研究了两个初始为|Ψa(0)＞和|Φa(0)＞纠缠态的原子与光场作用过程中原子的纠缠演化特性.讨论了不同初始原子纠缠度,不同耗散系数以及不同平均光子数对两原子纠缠度的影响.结果表明:①当原子初始处于|Ψa(0)＞类纠缠态时,其纠缠度随光场强度以及腔场衰减系数演化.当腔不存在耗散时,纠缠度呈周期性振荡;当腔存在耗散时,纠缠度呈衰减振荡并趋于稳定值;且光强越弱,其稳定值越大;衰减系数越大纠缠达到稳定值所需时间越短.②原子初始处于|Φa(0)＞类纠缠态时,其纠缠度只与原子初始纠缠度有关,不随其他因素变化.     

Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state

We have investigated the effect of counter-rotating terms on the dynamics of entanglement and quantum discord between two identical atoms interacting with a lossy single mode cavity field for a system initially in a vacuum state. The counter-rotating terms are found to lead to steady states in the long-time limit which can have high quantum discord, but have no entanglement. The effect of cavity decay rate on this steady-state quantum discord has been also investigated, surprisingly, the increase in cavity decay rate is found to enhance the steady-state quantum discord.     

Decoherence of interacting qubits in contact with a common environment

Decoherence of interacting two qubits placed under the influence of a common environment is studied by means of the quantum master equation, where the two qubits interact with each other via the XY-coupling and the two-qubit system has the dephasing coupling with the environment. It is shown that when the asymmetry of the interaction between the two-qubit system and environment is not small, the qubit-qubit interaction significantly affects the dephasing of the two-qubit system. To examine such an interaction effect, the decay of two-qubit entanglement is calculated. It is found that the qubit-qubit interaction makes not only the decay of entanglement small but also the period of the oscillatory behaviour short.     

Classical-driving-assisted coherence dynamics and its conservation

We investigate the quantum coherence and quantum entanglement dynamics of a classical driven single atom coupled to a single-mode cavity. It is shown that the transformation between the atomic coherence and the atom-field entanglement exists, and can be improved by adjusting the classical driving field. The joint evolution of two identical single-body systems is also studied. The results show the quantum coherence transfers among composite subsystems, and the coherence conservation of composite subsystems is obtained. Moreover, the classical driving field can be used to suppress the decay of the coherence and entanglement, owing to considering the leaky cavity. The non-Markovian dynamics of the system is also discussed finally.     

Dynamics of Quantum Discord of Two-Qubit Coupled with a Vacuum Cavity

The dynamical behaviors of quantum discord between two atoms coupled with a vacuum cavity are investigated. If the two qubits are initially prepared in two extended Werner-like states, the quantum discord and entanglement can be numerically calculated. There are remarkable differences between the time evolutions of the quantum discord and entanglement under the same conditions. These results imply that quantum discord is not zero for some unentangled states and in some regions entanglement can disappear completely. A large amount of quantum discord exists between the two-qubit. Thus, the quantum discord is more robust than entanglement for the quantum system exposed to the environment. The quantum discord shows sudden change and its existence depends on the initial state of the system. This property of quantum discord may have important implications for experimental characterization of quantum phase transitions.     

Decoherence from a spin chain with Dzyaloshinskii—Moriya interaction

We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya interaction.In the case of a two-qubit with an initial pure state,quantum correlations decay to zero at the critical point of the environment in a very short time.In the case of a two-qubit with initial mixed state,it is found that quantum discord may get maximized due to the quantum critical behavior of the environment,while entanglement vanishes under the same condition.Besides,we observed a sudden transition between classical and quantum decoherence when only a single qubit interacts with the environment.The effects of Dzyaloshinsky-Moriya interaction on quantum correlations are considered in the two cases.The decay of quantum correlations is always strengthened by Dzyaloshinsky-Moriya interaction.     

Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain

This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.     

Non-Markovian effects on entanglement dynamics in lossy cavities

We consider the non-markovian entanglement dynamics of two independent atoms, each off-resonantly coupling with a zero temperature reservoir. For two types of initial entanglement, corresponding to spin correlated and anti-correlated Bell-like states |φ〉 and |ψ〉, we study the dependence of the two-qubit entanglement transfer on both the off-resonant interactions and the cavity pseudomode decay. The speed of the entanglement transfer is related to the choice of the atom detuning from the cavity pseudomode, the cavity pseudomode decay and the relative coupling. Furthermore, compared to the ideal cavities, entanglement transfer and sudden death can not be prevented using off-resonant interactions in the lossy cavities, and the conservation rules are always satisfied in the off-resonant and lossy system.     

Quantum Discord for Two-Qubit System in a Symmetry-Broken Environment

In contrast with the entanglement, we study the quantum discord dynamics of the two-qubit system in a symmetry-broken environment consisting of a fermionic bath. The quantum discord decay induced by the bath is analysed. By considering the two qubits that are initially prepared in the different X-states, we find that the behaviors of quantum discord and entanglement are different, the robustness of quantum discord depends on the initial state prepared in.     

耦合双Tavis-Cummings模型中的纠缠演化和转移特性

研究了由光纤模连接的两个Tavis-Cummings模型中纠缠演化和纠缠转移的特性。结果表明,初始两原子间的纠缠可转移为另两原子间的纠缠,在纠缠转移过程中,光纤模起到中间传递的作用。纠缠的转移与初始两原子间的纠缠、原子与腔场的耦合强度以及光纤模与腔场的耦合强度、原子与腔场的失谐量和腔场耗散有关。初始纠缠决定了另两原子间纠缠产生的大小;在原子与腔场的耦合强度一定的条件下,随着光纤模与腔场耦合强度的增强,纠缠转移的时间缩短,且产生的纠缠值增加;腔场耗散对纠缠演化的衰减影响是显著的,而失谐量的增加可以有效地抑制这一现象。在整个纠缠转移过程中,系统中其他任两子体系间的纠缠起到了桥梁的作用,实现了两量子纠缠态的远程传递和制备。     

量子关联与原子间相互作用距离关系的研究

本文将两个二能级原子注入一个腔中,用共生纠缠的方法来度量两原子之间的纠缠并推出它们之间的量子失协,还给出了原子与环境之间的共生纠缠与量子失协的计算公式,讨论了原子自发衰变率的变化对量子纠缠及失协的影响,及不同的初始状态情况下,纠缠及失协随原子距离的演化情况。结果表明：原子自发衰变率减小,原子与环境之间的量子纠缠及失协增加;选择不同的初态,可以控制原子间出现纠缠死亡的现象或量子失协为零的状态。     

量子关联与原子间相互作用距离关系的研究

本文将两个二能级原子注入一个腔中,用共生纠缠的方法来度量两原子之间的纠缠并推出它们之间的量子失协,还给出了原子与环境之间的共生纠缠与量子失协的计算公式,讨论了原子自发衰变率的变化对量子纠缠及失协的影响,及不同的初始状态情况下,纠缠及失协随原子距离的演化情况.结果表明:原子自发衰变率减小,原子与环境之间的量子纠缠及失协增加;选择不同的初态,可以控制原子间出现纠缠死亡的现象或量子失协为零的状态.     

量子关联与原子间相互作用距离关系的研究

本文将两个二能级原子注入一个腔中,用共生纠缠的方法来度量两原子之间的纠缠并推出它们之间的量子失协,还给出了原子与环境之间的共生纠缠与量子失协的计算公式,讨论了原子自发衰变率的变化对量子纠缠及失协的影响,及不同的初始状态情况下,纠缠及失协随原子距离的演化情况。结果表明：原子自发衰变率减小,原子与环境之间的量子纠缠及失协增加;选择不同的初态,可以控制原子间出现纠缠死亡的现象或量子失协为零的状态。     

Disentanglement Dynamics in Nonequilibrium Environments

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.