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.     

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.     

General Non-Markovian Quantum Dynamics

A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. A wide class of the exactly solvable models of non-Markovian quantum dynamics is suggested. These models describe open (non-Hamiltonian) quantum systems with general form of nonlocality in time. To describe these systems, the Lindblad equations for quantum observable and states are generalized by taking into account a general form of nonlocality. The non-Markovian quantum dynamics is described by using integro-differential equations with general fractional derivatives and integrals with respect to time. The exact solutions of these equations are derived by using the operational calculus that is proposed by Yu. Luchko for general fractional differential equations. Properties of bi-positivity, complete positivity, dissipativity, and generalized dissipativity in general non-Markovian quantum dynamics are discussed. Examples of a quantum oscillator and two-level quantum system with a general form of nonlocality in time are suggested.     

Quantum statistical effects in nuclear reactions,fission, and open quantum systems

Quantum diffusion equations with time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytical formulas for calculating friction and diffusion coefficients in nuclear processes are obtained. The asymptotics of the transport coefficients and of the correlation functions are investigated. The problem of correlation decay in quantum dissipative systems is studied. A comparative analysis of diffusion coefficients for the harmonic and inverted oscillators is performed. The role of quantum statistical effects during passage through a parabolic potential barrier is investigated. Sets of diffusion coefficient assuring the purity of states at any time instant are found in cases of non-Markovian dynamics. The influence of different sets of transport coefficients on the rate of decay from a metastable state is studied in the framework of the master equation for reduced density matrices describing open quantum systems. The approach developed is applied to investigation of fission processes and the processes of projectile-nuclei capture by target nuclei for bombarding energies in the vicinity of the Coulomb barrier. The influence of dissipation and fluctuation on these processes is taken into account in a self-consistent way. The evaporation residue cross sections for asymmetric fusion reactions are calculated from the derived capture probabilities averaged over all orientations of the deformed projectile and target nuclei.     

Non-Markovian dynamics of open quantum systems: Stochastic equations and their perturbative solutions

We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born–Markov or rotating wave approximations (RWA). This includes master equations of the (asymptotically) stationary, periodic, and time-nonlocal type. We provide proofs on the validity and meaningfulness of the late-time perturbative master equation and on the preservation of complete positivity despite a general lack of Lindblad form. More specifically, we show how the algebraic generators satisfy the theorem of Lindblad and Gorini, Kossakowski and Sudarshan, even though the dynamical generators do not. These proofs ensure the mathematical viability and physical soundness of solutions to non-Markovian processes. Within the same formalism we also expand upon known results for non-Markovian corrections to the quantum regression theorem. Several directions where these results can be usefully applied to are also described, including the analysis of near-resonant systems where the RWA is inapplicable and the calculation of the reduced equilibrium state of open systems.     

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.     

Dynamical learning of non-Markovian quantum dynamics

We study the non-Markovian dynamics of an open quantum system with machine learning.The observable physical quantities and their evolutions are generated by using the neural network.After the pre-training is completed,we fix the weights in the subsequent processes thus do not need the further gradient feedback.We find that the dynamical properties of physical quantities obtained by the dynamical learning are better than those obtained by the learning of Hamiltonian and time evolution operator.The dynamical learning can be applied to other quantum many-body systems,non-equilibrium statistics and random processes.     

Boson–boson pure-dephasing model with non-Markovian properties

In this paper, we discuss the mechanism of pure-dephasing process with a newly proposed boson–boson model, namely, a bosonic field coupled to another bosonic bath in thermal equilibrium. Our model is fully solvable and can reproduce the pure-dephasing process which is usually described by the well-known spin–boson model, therefore offering a new perspective to understanding decoherence processes in open quantum systems of high dimension. We also show that this model admits a generically non-Markovian dynamics with respect to various different non-Markovian characterizations, i.e., the criteria based on divisibility, quantum regression formula and Wigner function, respectively. The criterion based on Wigner function is firstly proposed in this paper. For the case that the particle number of the pure-dephasing system is constrained to be 0 or 1, we analytically prove its equivalence to the criteria based on trace distance and divisibility.     

Full counting statistics in strongly interacting systems: non-Markovian effects

We present a theory of full counting statistics for electron transport through interacting electron systems with non-Markovian dynamics. We illustrate our approach for transport through a single-level quantum dot and a metallic single-electron transistor to second order in the tunnel coupling, and discuss under which circumstances non-Markovian effects appear in the transport properties.     

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.     

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.     

Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.     

Cotunneling current and shot noise in quantum dots

We derive general expressions for the current and the shot noise, taking into account non-Markovian memory effects. In generalization of previous approaches, our theory is valid for an arbitrary Coulomb interaction and coupling strength and is applicable to quantum dots and more complex systems such as molecules. A fully consistent diagrammatic expansion up to second order in the coupling strength, taking into account cotunneling processes, allows for a study of transport in an intermediate coupling strength regime relevant to many current experiments. We discuss a single-level quantum dot as a first example, focusing on the Coulomb-blockade regime where the cotunneling processes dominate. We find super-Poissonian shot noise due to inelastic spin-flip cotunneling processes at an energy scale different from the one expected from first-order calculations.     

Quantum Maps with Memory from Generalized Lindblad Equation

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.     

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.     

Divergence of fermionic correlations under non-Markovian noise in a non-inertial frame

Non-Markovian dynamics of correlations of fermionic systems is investigated beyond the single-mode approximations in a non-inertial frame. Two well known correlation measures, quantum discord and geometric quantum discord, are analyzed for the fermionic states influenced by the non-Markovian noise. Persistence of discord is seen for longer times depending upon the level of mixedness of the fermionic system. The dynamics of the fermionic systems heavily depends upon the degree of white noise. It is shown that fermionic systems remain dependent upon the choice of Unruh modes (_qR$q_R$) beyond the single-mode approximations under non-Markovian noise. Quantum discord is found to be more robust as compared to the geometric quantum discord. Furthermore, the non-Markovian effects are more stronger than the acceleration of Bob, the accelerated partner.     

Non-markovian decoherence of localized nanotube excitons by acoustic phonons

We demonstrate that electron-phonon interaction in quantum dots embedded in one-dimensional systems leads to pronounced, non-Markovian decoherence of optical transitions. The experiments that we present focus on the line shape of photoluminescence from low-temperature axially localized carbon nanotube excitons. The independent boson model that we use to model the phonon interactions reproduces with very high accuracy the broad and asymmetric emission lines and the weak red-detuned radial breathing mode replicas observed in the experiments. The intrinsic phonon-induced pure dephasing of the zero-phonon line is 2 orders of magnitude larger than the lifetime broadening and is a hallmark of the reduced dimensionality of the phonon bath. The non-Markovian nature of this decoherence mechanism may have adverse consequences for applications of one-dimensional systems in quantum information processing.     

Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.     

Time-Dependent Dephasing and Quantum Transport

The investigation of the phenomenon of dephasing assisted quantum transport, which happens when the presence of dephasing benefits the efficiency of this process, has been mainly focused on Markovian scenarios associated with constant and positive dephasing rates in their respective Lindblad master equations. What happens if we consider a more general framework, where time-dependent dephasing rates are allowed, thereby, permitting the possibility of non-Markovian scenarios? Does dephasing-assisted transport still manifest for non-Markovian dephasing? Here, we address these open questions in a setup of coupled two-level systems. Our results show that the manifestation of non-Markovian dephasing-assisted transport depends on the way in which the incoherent energy sources are locally coupled to the chain. This is illustrated with two different configurations, namely non-symmetric and symmetric. Specifically, we verify that non-Markovian dephasing-assisted transport manifested only in the non-symmetric configuration. This allows us to draw a parallel with the conditions in which time-independent Markovian dephasing-assisted transport manifests. Finally, we find similar results by considering a controllable and experimentally implementable system, which highlights the significance of our findings for quantum technologies.