非马尔科夫环境中各向异性海森堡自旋链的量子失协

利用量子失协方法研究在非马尔科夫环境中具有时变磁场的两比特各向异性海森堡XYZ模型量子失协的动力学演化。海森堡XYZ系统的初始态为最大纠缠态 $\left|\psi_{A B}\right\rangle=(1 / \sqrt{2})(|11\rangle+|00\rangle)$ , 利用非马尔科夫量子态扩散方法解析求解非马尔科夫主方程, 得出系统的约化密度矩阵; 然后代入量子失协公式得出系统量子失协的演化动力学。讨论自旋耦合强度、环境关联系数γ和余弦磁场强度B对量子失协动力学的影响。研究发现: 当环境关联系数γ较小时, 系统的量子失协明显呈现上升趋势, 因此可以表明非马尔科夫环境具有增加系统量子失协的作用。同时较大的自旋耦合系数J和J_Z以及余弦磁场强度B也具有增加系统量子失协的作用。     

Quench of non-Markovian coherence in the deep sub-Ohmic spin–boson model: A unitary equilibration scheme

The deep sub-Ohmic spin–boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly quenched even in the coherent regime, in which the non-Markovian feature dominates. With this finding we come up with a novel way to implement the unitary equilibration, the essential term of the eigenstate-thermalization hypothesis, through a short-time evolution of the model.     

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.     

Non-Markovian diffusion equations and processes: Analysis and simulations

In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation can be interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the memory kernel K(t). We develop several applications and derive the exact solutions. We consider different stochastic models for the given equations providing path simulations.     

Quantum Non-Markovianity via the Covariance Matrix

In this paper, we propose a new characterization of non-Markovian quantum evolution based on the covariance matrix. The fundamental properties of covariance matrices are elucidated. The measure captures quite directly the characteristics of non-Markovianity from the perspective of uncertainty. We consider several typical examples and compare the covariance matrix characterization of quantum non-Markovianity with Fisher-information matrix, divisibility and the Breuer-Laine-Piilo characterization of quantum non-Markovianity.     

Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process

Coherence is a key resource in quantum information science.Exactly understanding and controlling the variation of coherence are vital for implementation in realistic quantum systems.Using P-representation of density matrix,we obtain the analytical solution of the master equation for the classical states in the non-Markovian process and investigate the coherent dynamics of Gaussian states.It is found that quantum coherence can be preserved in such a process if the coupling strength between system and environment exceeds a threshold value.We also discuss the characteristic function of the Gaussian states in the non-Markovian process,which provides an inevitable bridge for the control and operation of quantum coherence.     

Fermionic-mode entanglement in non-Markovian environment

We evaluate the non-Markovian effects on the entanglement dynamics of a fermionic system interacting with two dissipative vacuum reservoirs. The exact solution of density matrix is derived by utilizing the Feynman–Vernon influence functional theory in the fermionic coherent state representation and the Grassmann calculus, which are valid for both the fermionic and bosonic baths, and their difference lies in the dependence of the parity of the initial states. The fermionic entanglement dynamics is presented by adding an additional restriction to the density matrix known as the superselection rules. Our analysis shows that the usual decoherence suppression schemes implemented in qubits systems can also be achieved for systems of identical fermions, and the initial state proves its importance in the evolution of fermionic entanglement. Our results provide a potential way to decoherence controlling of identical fermions.     

Rise of quantum correlations in non-Markovian environments in continuous-variable systems

We investigate the time evolution of quantum correlations, which are measured by Gaussian quantum discord in a continuous-variable bipartite system subject to common and independent non-Markovian environments. Considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that quantum correlations can be created during the non-Markovian evolution, which is different from the Markovian process. Furthermore, we find that the temperature is a key factor during the evolution in non-Markovian environments. For common reservoirs, a maximum creation of quantum correlations may occur under an appropriate temperature. For independent reservoirs, the non-Markovianity of the total system corresponds to the subsystem whose temperature is higher. In both common and independent environments, the Gaussian quantum discord is influenced by the temperature and the photon number of each mode.     

Non-Markovianity and Indivisible Quantum dynamics of a Apin-S System

Using a measure for the divisibility of a dynamical map,we study the non-Markovian character of a quantum evolution of a spin-S system,which is in an external field and weakly coupled to a bosonic bath with a certain temperature.The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation.Besides the influence of the environmental spectral density function,the external field and low temperatures can afect the quantum non-Markovianity.It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.     

Exact solution for a non-Markovian dissipative quantum dynamics

We provide the exact analytic solution of the stochastic Schr?dinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.     

Non-Markovianity and Indivisible Quantum dynamics of a Apin-S System

Using a measure for the divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a spin-S system, which is in an external field and weakly coupled to a bosonic bath with a certain temperature. The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. Besides the influence of the environmental spectral density function, the external field and low temperatures can affect the quantum non-Markovianity. It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.     

Non-Markovian thermalisation of a two-level atom

We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima-Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.     

Quantum correlation dynamics of three non-coupled two-level atoms in different reservoirs

Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density.For three atoms initially prepared in Greenberger-Horne-Zeilinger-type state,quantum correlation dynamics in a Markovian reservoir is compared with that in a nonMarkovian reservoir.By increasing detuning quantity in the non-Markovian reservoir,three-atom correlation dynamics measured by negative eigenvalue presents a trapping phenomenon which provides long-time quantum entanglement.Then we compare the correlation dynamics of three atoms with that of two atoms,measured by quantum entanglement and quantum discord for an initial robuster-entangled type state.The result further confirms that quantum discord is indeed different from quantum entanglement in identifying quantum correlation of many bodies.     

Non-Markovian relaxation in an open quantum system

Non-Markovian dynamics in open quantum systems is characterized by a time-non-locality in the equation of motion valid for the reduced density operator. An expansion of this density matrix equation with respect to Laguerre polynomials is used to tackle the time-non-locality. The applicability and the numerical limitations of the method are discussed in detail. In order to illuminate the characteristics of non-Markovian dynamics the reference example is studied of a single quantum degree of freedom moving in a harmonic potential and being embedded in a heat bath. If interpreted as the photoinduced dynamics of nuclear motion in polyatomic molecules we can suggest two clear signatures of non-Markovian dynamics observable in ultrafast optical experiments, firstly a pronounced and somewhat irregular oscillatory behavior of the vibrational level populations, and secondly a separation of the vibrational wavepacket into a double-structure. Received 12 April 2000 and Received in final form 2 September 2000     

Mutual preservation of entanglement

We study a generalized double Jaynes–Cummings (JC) model where two entangled pairs of two-level atoms interact indirectly. We show that there exist initial states of the qubit system so that two entangled pairs are available at all times. In particular, the minimum entanglement in the pairs as a function of the initial state is studied. Finally, we extend our findings to a model consisting of multi-mode atom–cavity interactions. We use a non-Markovian quantum state diffusion (QSD) equation to obtain the steady-state density matrix for the qubits. We show that the multi-mode model also displays dynamical preservation of entanglement.     

Solving non-Markovian open quantum systems with multi-channel reservoir coupling

We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein–Uhlenbeck reservoir correlations numerically.     

非马尔科夫耗散系统长时演化下的极限环振荡现象

本文研究结构化环境中非马尔科夫耗散系统在长时演化下可能出现的极限环振荡现象. 对于欧姆型谱密度环境中的二能级系统, 由于体系只允许一个束缚态模, 给定初态系统在Bloch空间的长时演化将收敛于一个极限环. 研究揭示了极限环半径与环心位置同环境谱密度函数间的关系. 对于多带光子晶体环境中的二能级系统, 由于其可以存在多个束缚态, 研究展现了系统在长时演化下可能出现的收敛于环面或周期或准周期的振荡行为. 有关环面的特征量与环境谱密度间的量化关系同样得以刻画. 论文随后讨论了两比特系统关联量在局域非马尔科夫耗散环境中长时演化可能出现的特征行为.     

Measurement-induced multipartite entanglement for distant four-level atoms in Markovian and non-Markovian environments

In this paper, we propose a scheme for generating multipartite entanglement of distant four-level atoms separately trapped in individual cavities, each of which is coupled to a non-Markovian reservoir. The entanglement of atoms is generated by measuring the photons leaking from cavities. In non-Markovian environments, we derive dynamical evolution of the entanglement and obtain the condition of generating the long-living multipartite maximally entangled state. When the condition is not satisfied, by introducing a time-varying coupling strength, the maximal multipartite entangled state can also be generated.     

Dynamical Change of Quantum Fisher Information of Cavity-Reservoir Systems

We study the quantum Fisher information(QFI) dynamics of the phase parameter in the enlarged cavityreservoir systems at zero temperature under two situations of large N limit and non-Markovian environment,respectively.We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution.The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously.Moreover,we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.     

The population and decay evolution of a qubit under the time-convolutionless master equation

We consider the population and decay of a qubit under the electromagnetic environment. Employing the time-convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper.