Failure of free energy relation under non-Markovian heat bath temperature change

We investigate the free energy relation for a system contacting with a non-Markovian heat bath and find that the validity of the relation sensitively depends on the non-Markovian memory effect, which is especially related to the initial preparation effect. This memory effect drives the statistical distribution of the system out of the initial preparation, even if the system starts from an equilibrium state. This leads to the violation of the free energy relation. A possible way of eliminating this memory effect is proposed.     

Failure of the free energy relation under a non-Markovian heat bath temperature change

We investigate the free energy relation for a system contacting with a non-Markovian heat bath and find that the validity of the relation sensitively depends on the non-Markovian memory effect, which is especially related to the initial preparation effect. This memory effect drives the statistical distribution of the system out of the initial preparation, even if the system starts from an equilibrium state. This leads to the violation of the free energy relation. A possible way of eliminating this memory effect is proposed.     

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.     

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.     

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.     

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.     

Orbit Tracking of Quantum State for Non-Markovian Quantum System Based on Model Reference Adaptive Control

Utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and investigate the orbit tracking of quantum state for non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz-Drude regularization is numerically studied for a two-level system. The simulations show that the controlled quantum system will track the target orbit with a small oscillation due to the non-Markovian environmental memory effect, which indicates the orbit tracking of non-Markovian quantum system is incomplete.     

Modulation of Entanglement for Coupled Superconducting Qubits Under Non-Markovian Environment

The evolution of entanglement decoherence is investigated for a coupled superconducting qubit under non-Markovian environment by utilizing a commensal entanglement degree. The results show that, owing to the memory feedback effect of environment, the entanglement degree of the coupled qubits at the thermal equilibrium always monotonously tends to zero so that entanglement sudden death occurs briefly in the non-Markovian process. Different from the Markovian process, stronger the dissipation is, faster the entanglement sudden death is. We find that, furthermore, the interaction between the qubits results generally in reduction of entanglement degree in the quantum system. With some special initial states or initial phase angles, however, the influence of the interaction between qubits on the system entanglement degree can be avoided.     

Entanglement Protection for Two-Qubit in a Non-Markovian Common Bath

In this paper, we propose a scheme to protect quantum entanglement and coherence from a non-Markovian noisy environment. By applying two quantum weak measurements before and after sending the quantum state into the noisy channel, the quantum state can be “pushed” closer to a decoherence free state thus suffer less decoherence in the time evolution. After the time evolution the second weak measurement can partially retrieve the original information encoded in the quantum system. Our study is based on a non-Markovian dynamic equation which allows us to investigate the impact of the memory effect on the performance of the protection scheme. We analyze several factors that may affect the protection efficiency. The results suggest that two measurement strengths should be chosen in a linear relation but the ratio is not one. Besides, we also show the memory effect can drastically improve the protection efficiency.     

Non-Markovian Two-Time Correlation Dynamics and Nonergodicity

The two-time correlation functions of the coordinate and velocity of a non-Markovian harmonic particle are derived analytically. They are decomposed into the components of differences between the initial variances and the equilibrium of the particle; in particular, the dependence of a random force on the initial preparation of the system is included. Using those expressions, we simultaneously investigate nonstationary, nonergodic, and nonequilibrium features of a forced system. It is demonstrated that the result of combining the oscillating relaxation and the initial preparation-dependent noise leads to breakdown of both ergodicity and equilibration of a forced system. The finite-size effect of a coupled-oscillator-chain heat bath is also discussed.     

Discord and entanglement in non-Markovian environments at finite temperatures

The dynamic evolutions of the discord and entanglement of two atoms immersed in two independent Lorentzian reservoirs at zero and finite temperatures have been investigated by using the time-convolutionless master-equation method.Our results show that,nonzero temperature can induce the entanglement sudden death and accelerate the decays of discord and entanglement.The discord and the entanglement have different robustness for different initial states and their robustness may change under certain conditions.When both the non-Markovian effect and detuning are present simultaneously,due to the memory and feedback effect of non-Markovian reservoirs,the discord and entanglement can be effectively protected even at nonzero temperature by increasing the non-Markovian effect and the detuning.     

Reducing the Entropic Uncertainty via Non-Markovian Effect and Detuning in the Presence of Quantum Memory ∗

The influence of non-Markovian effect and detuning on the entropic uncertainty in the presence of quantum memory is studied by the time-convolutionless master-equation approach. The result shows that the entropic uncertainty in the presence of quantum memory is obviously dependent on both detuning and non-Markovian effect. The bigger the detuning is and the stronger the non-Markovian effect is, the smaller the entropic uncertainty is. Its physical explanation is that the known quantum information stored in the quantum memory can reduce or eliminate the entropic uncertainty about the measurement outcomes of another particle, which is entangled with the quantum memory.     

原子系统中偶极-偶极相互作用对量子存储支撑熵不确定度的调控研究

本文研究了Markovian过程和non-Markovian过程两种情况下,原子系统中偶极-偶极(D-D)相互作用和失谐量对两原子系统量子存储支撑(QMA)熵不确定度的调控作用.与Markovian过程相比,在non-Markovian过程中,由于库环境的记忆效应使得具有D-D相互作用的两原子系统QMA熵不确定度的演化行为呈现出振荡上升现象,且熵不确定度的上升趋势得到减缓,从而抑制了由系统量子噪声引起的退相干效应.此外,D-D相互作用对两原子系统QMA熵不确定度具有显著的调控能力,且D-D相互作用比失谐量的调控能力更强.     

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。     

Microscopic preparation and macroscopic motion of a Brownian particle

We study the effect of a non-equilibrium state of the bath on the macroscopic motion of a Brownian particle (B.p.) in a linear chain. The macroscopic motion is described by a stochastic process which is non-Markovian and nonstationary due to the initial non-equilibrium of the bath. We derive generalized Langevin equations for this proces. We solve them explicitely for the case of a free B.p. and discuss the resulting mean values. A Markov approximation is valid only in the long time region, non-Markovian transients cannot be neglected. In the long time region the non-equilibrium state of the bath has the same effect as a modified macroscopic initial condition for the B.p.     

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.     

Quantum Information Scrambling in Non-Markovian Open Quantum System

In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.     

Nonergodic Brownian Motion

The long-time behavior of a system is suggested to confirm nonergodicity of non-Markovian Brownian dynamics, namely, whether the stationary probability density function （PDF） of the system characterized mainly by low moments of variables depends on the initial preparation. Thus we classify nonergodic Brownian motion into two classes： the class-I is that the PDF of a force-free particle depends on the initial velocity and the equilibration can be recovered through a bounded potential; while the PDF in the class-H depends on the initial coordinate and the equilibration can not be approached by introducing any potential. We also compare our result with the conditions of three kinds for ergodicity.     

Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field

For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad’s form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.     

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.