Dynamics of two levitated nanospheres nonlinearly coupling with non-Markovian environment

The dynamics of two nanospheres nonlinearly coupling with non-Markovian reservoir is investigated. A master equation of the two nanospheres is derived by employing quantum state diffusion method. It is shown that the nonlinear coupling can improve the non-Markovianity. Due to the sharing of the common non-Markovian environment, the state transfer between the two nanospheres can be realized. The entanglement and the squeezing of the individual mode, as well as the jointed two-mode are analyzed. The present system can be realized by trapping two nanospheres in a wideband cavity, which might provide a method to study adjustable non-Markovian dynamics of mechanical motion.     

Non-Markovian dynamics of spin squeezing

We evaluate the spin squeezing dynamics of N independent spin-1/2 particles with exchange symmetry. Each particle couples to an individual and identical reservoir. We study the time evolution of spin squeezing under the influence of different decoherence. The spin squeezing property vanishes with evolution time under Markovian decoherence, while it collapses quickly and revives under non-Markovian decoherence. As spin squeezing can be regarded as a witness of multipartite entanglement, our scheme shows the collapses and revivals of multipartite entanglement under the influence of non-Markovian decoherence.     

Non-Markovian effect on remote state preparation

Memory effect of non-Markovian dynamics in open quantum systems is often believed to be beneficial for quantum information processing. In this work, we employ an experimentally controllable two-photon open system, with one photon experiencing a dephasing environment and the other being free from noise, to show that non-Markovian effect may also have a negative impact on quantum tasks such as remote state preparation: For a certain period of controlled time interval, stronger non-Markovian effect yields lower fidelity of remote state preparation, as opposed to the common wisdom that more information leads to better performance. As a comparison, a positive non-Markovian effect on the RSP fidelity with another typical non-Markovian noise is analyzed. Consequently, the observed dual character of non-Markovian effect will be of great importance in the field of open systems engineering.     

Non-Markovian entanglement transfer to distant atoms in a coupled superconducting resonator

We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits,which are embedded in a coupled superconducting resonator. The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion(NMQSD) method. Based on the solution, we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time. That is to say, the non-Markovian environment can enhance the entanglement transfer. It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated intercavity coupling. Moreover, with the initial anti-correlated state, the entanglement between the cavity fields can be almost completely transferred to the separated atoms. Lastly, we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.     

利用量子相干性判定开放二能级系统中非马尔可夫性

从量子相干性包括l₁ norm相干性和量子相对熵相干性的角度建立了判定开放量子系统中非马尔可夫过程的方法, 并给出了相应的判别条件. 作为它们的具体应用, 研究了一个两能级系统分别经历相位衰减通道、 随机幺正通道和振幅耗散通道作用时对应的非马尔可夫过程发生必须满足的条件. 对于三种通道模型, 得到了l₁ norm相干性对系统任意态非马尔可夫过程发生的判别条件, 并发现在相位衰减通道和振幅耗散通道中其非马尔可夫过程发生 的条件与用其他方式如信息回流、可分性和量子互熵给出的条件是相同的, 而在随机幺正通道中给出了一个新的且不完全等价于基于信息回流和可分性对应的条件. 至于量子相对熵相干性, 在相位衰减通道中得到了对系统任意态的非马尔可夫过程发生的具体条件, 并发现该条件也等同于基于信息回流、可分性和量子互熵给出的条件. 而在随机幺正通道和振幅耗散通道中得到了系统最大相干态对应的非马尔可夫过程发生的条件.     

Entropy production and nonequilibrium stationarity in quantum dynamical systems. Physical meaning of van Hove limit

With aid of the so-called dilation method, a concise formula is obtained for the entropy production in the algebraic formulation of quantum dynamical systems. In this framework, the initial ergodic state of an external force system plays a pivotal role in generating dissipativity as a conditional expectation. The physical meaning of van Hove limit is clarified through the scale-changing transformation to control transitions between microscopic and macroscopic levels. It plays a crucial role in realizing the macroscopic stationarity in the presence of microscopic fluctuations as well as in the transition from non-Markovian (groupoid) dynamics to Markovian dissipative processes of state changes. The extension of the formalism to cases with spatial and internal inhomogeneity is indicated in the light of the groupoid dynamical systems and noncommutative integration theory.     

Quantum Discord Dynamics of Three Qubits in Non-Markovian Environments

We investigate the dynamics of palrwise quantum discord （QD） for a mixed three-qubit W-type state in three independent non-Markovian reservoirs at zero temperature, each of which is modeled by a leaky cavity with Lorentzian spectral density. The influence of the environment＇s amount of non-Markovianity, the detuning between the qubit frequency and the cavity centre frequency, and the purity of the initial state on the QD dynamics are analyzed in detail. It is found that in the non-Maxkovian regime the system-reservoir interactions induce QD revivals and oscillations no matter whether the detuning is zero or not. Moreover, QD can be preserved for a long time if the non-Markovian condition and the detuning condition are satisfied simultaneously.     

Exact c-number representation of non-Markovian quantum dissipation

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr?dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born-Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.     

二能级系统的马尔可夫与非马尔可夫方法比较

分别用马尔可夫与非马尔可夫方法推导出二能级系统与库相互作用的耗散动力学,并把失谐谱密度与一个光子带隙的谱密度下的计算结果与精确解进行比较。对于失谐谱密度,分别讨论在马尔可夫与非马尔可夫库的激发态布居数,发现无论是短时的弱耦合区域,还是长时间的强耦合区域,非马尔可夫方法比马尔可夫方法更加接近精确解,而马尔可夫近似主要适用于弱耦合条件;对于光子带隙谱密度,主要考虑了小带宽的布居数,结果显示马尔可夫方法主要适用于弱耦合条件,而非马尔可夫方法主要适用于强耦合情形。结果表明:对于不同谱密度、不同的耦合区域,只有选择合适的马尔可夫或非马尔可夫方法才能精确描述系统的动力学。     

Restoration of Coherence by Local PT-Symmetric Operator

In this work, we mainly investigate effect of PT-symmetric operation on the dynamics of the relative entropy of coherence for a two-level system within non-Markovian environments, and put forward a feasible physical scheme to recover coherence by means of optimal PT-symmetric operation. The results show that the damaged quantum coherence can be restored to a large extent. Furthermore, the freezing phenomenon of the coherence can be detected by using the optimal PT-symmetric operation strength within the non-Markovian environments.

     

非马尔科夫环境下耦合超导量子系统纠缠演化的数值研究

基于耦合超导量子比特系统模型下,在非马尔科夫环境中利用共生纠缠的方法分析了耦合系统纠缠的产生及其动力学的演化。研究了不同初始纠缠态下的纠缠猝死(ESD)和纠缠再生(ESB)现象;主要分析了系统耦合强度、库的截止频率与系统的振荡频率间的比值、温度和约瑟夫森能级差对纠缠演化的影响。结果表明:系统纠缠取决于初始纠缠态和系统的耦合强度J,并且通过调节以上非马尔科夫环境的相干参数可以延长解纠缠时间来确保量子计算过程中的应用和量子信息的实现。     

Effect of PT-Symmetric Operator on Coherence Under the Non-Markovian Environments

In this work, we mainly investigate effect of PT-symmetric operation on the dynamic behavior of the relative entropy of coherence for a two-level system within non-Markovian environments and put forward a feasible physical scheme to recover coherence by utilizing optimal PT-symmetric operation. The results show that the damaged quantum coherence can be effectively restored under influence of the non-Markovian regimes. Furthermore, the freezing phenomenon of the coherence can be detected by using the optimal PT-symmetric operation strength within the non-Markovian environments.

     

Regularization of Quantum Relative Entropy in Finite Dimensions and Application to Entropy Production

The fundamental concept of relative entropy is extended to a functional that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost all important properties of ordinary relative entropy such as joint convexity and contractivity under completely positive quantum dynamical semigroup time evolution. On this basis a generalized formula for entropy production is proposed, the applicability of which is tested in models of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves all types of states.     

Non-Markovian quantum jumps

Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo wave function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump approach circumvents this problem and provides an efficient unraveling of the ensemble dynamics.     

Correlations,Information Backflow,and Objectivity in a Class of Pure Dephasing Models

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen–Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some exhibit quantum Darwinistic features, while others show that no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system’s ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity.     

Non-Markovian Quantum Kinetics and Conservation Laws

A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle distribution function and the mean interaction energy are treated as independent nonequilibrium state parameters. The density operator method is used to derive a kinetic equation in second-order non-Markovian Born approximation and an evolution equation for the nonequilibrium quasi-temperature which is thermodynamically conjugated to the mean interaction energy. The kinetic equation contains a correlation contribution which exactly cancels the collision term in thermal equilibrium and ensures the energy conservation in nonequilibrium states. Explicit expressions for the entropy production in the non-Markovian regime and the time-dependent correlation energy are obtained.     

Population dynamics of excited atoms in non-Markovian environments at zero and finite temperature

The population dynamics of a two-atom system, which is in two independent Lorentzian reservoirs or in two independent Ohmic reservoirs respectively, where the reservoirs are at zero temperature or finite temperature, is studied by using the time-convolutionless master-equation method. The influences of the characteristics and temperature of a non-Markovian environment on the population of the excited atoms are analyzed. We find that the population trapping of the excited atoms is related to the characteristics and the temperature of the non-Markovian environment. The results show that, at zero temperature, the two atoms can be effectively trapped in the excited state both in the Lorentzian reservoirs and in the Ohmic reservoirs. At finite temperature, the population of the excited atoms will quickly decay to a nonzero value.     

Population Dynamics of Excited Atoms in Dissipative Cavities

Population dynamics of excited atoms in dissipative cavities is investigated in this work. We present a method of controlling populations of excited atoms in dissipative cavities. For the initial state |ee〉_AB|00〉_ab, the repopulation of excited atoms can be obtained by using atom-cavity couplings and non-Markovian effects after the atomic excited energy decays to zero. For the initial state |gg〉_AB|11〉_ab, the two atoms can also be populated to the excited states from the initial ground states by using atom-cavity couplings and non-Markovian effects. And the stronger the atom-cavity coupling or the non-Markovian effect is, the larger the number of repopulation of excited atoms is. Particularly, when the atom-cavity coupling or the non-Markovian effect is very strong, the number of repopulation of excited atoms can be close to one in a short time and will tend to a steady value in a long time.     

Dynamics of Quantum Entanglement in Reservoir with Memory Effects

The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects.The completely positive reduced dynamical map can be constructed in the Kraus representation.Quantum entanglement decays more slowly in the non-Markovian environment.The decoherence time for quantum entanglement can be markedly increased with the change of the memory kernel.It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants.     

Optimal control-based states transfer for non-Markovian quantum system

Utilizing the method of optimal control, we investigate the tactics of state transfer in the non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz–Drude regularization is numerically studied. Owing to the decoherence and memory effects of non-Markovian channel, the purity of quantum state attenuates damply in the free evolution. The numerical simulations indicate that arbitrary state transfer for non-Markovian system can be realized under the optimal control function by a proper external control field with a success rate of more than 98 percent. When the right control field and function is implemented, not only the decoherence is compensated completely but also the purity of quantum states are maintained in the process of state transfer.