Lech Jakobczyk
The dynamics of entanglement between two-level atoms immersed in a common photon reservoir at finite temperature is investigated. It is shown that in the regime of strong correlations there are nontrivial asymptotic states which can be interpreted in terms of thermal generalization of Werner states.
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We investigate the dynamical evolution of multipartite entanglement in tripartite systems with three qubits present in independent thermal reservoirs, modelled as infinite set of quantum harmonic oscillators. We show that the presence of temperature gradient between reservoirs play a significant role in robustness of multipartite correlation against environmental decoherence. Considering a bilinear form of interaction Hamiltonian, an exact expression for time evolved density matrix is presented. Interestingly, it is observed that the preservation duration of genuine multipartite concurrence fo…
Bell-inequality violation and entanglement, measured by Wootters' concurrence and negativity, of two qubits initially in Werner or Werner-like states coupled to thermal reservoirs are analyzed within the master equation approach. It is shown how this simple decoherence process leads to generation of states manifesting the relativity of two-qubit entanglement measures.
We study the quantum speed limit time for a two-qubit system interacts with indepen- dent and common reservoir. The system is initially prepared in a class of X-structure density matrix, namely the extended Werner-like states (EWL). We demonstrate that when reservoir enters to the non-Markovian regime, the quantum speed limit time de- crease more sharply in a common reservoir than independent reservoirs.
Entanglement estimation of Werner states with a quantum extreme learning machine
提出一种基于量子极限学习机（QELM）的协议，通过结合随机Werner态与储备池态并利用Ising哈密顿量演化，实现对Werner态纠缠量的估计，并验证了其鲁棒性及磁场参数对精度的影响。
We investigate the concurrence and Bell violation of the standard Werner state or Werner-like states in the presence of collective dephasing. It is shown that the standard Werner state and certain kinds of Werner-like states are robust against the collective dephasing, and some kinds of Werner-like states is fragile and becomes completely disentangled in a finite-time. The threshold time of complete disentanglement of the fragile Werner-like states is given. The influence of external driving field on the finite-time disentanglement of the standard Werner state or Werner-like states is discusse…
We study a single two-level atom interacting with a reservoir of modes defined by a reservoir structure function with a frequency gap. Using the pseudomodes technique, we derive the main features of a trapping state formed in the weak coupling regime. Utilising different entanglement measures we show that strong correlations and entanglement between the atom and the modes are in existence when this state is formed. Furthermore, an unexpected feature for the reservoir is revealed. In the long time limit and for weak coupling the reservoir spectrum is not constant in time.
We investigate the stationary entanglement and stationary nonlocality of two qubits collectively interacting with a common thermal environment. We assume two qubits are initially in Werner state or Werner-like state, and find that thermal environment can make two qubits become stationary nonlocality. The analytical relations among average thermal photon number of the environment, entanglement and nonlocality of two qubits are given in details. It is shown that the fraction of Bell singlet state plays a key role in the phenomenon that the common thermal reservoir can enhance the entanglement of…
Carnot's theorem poses a fundamental limit on the maximum efficiency achievable from an engine that works between two reservoirs at thermal equilibrium. We extend this result to the case of arbitrary nonthermal stationary reservoirs, even with quantum coherence. In order to do this we prove that a single nonthermal reservoir is formally equivalent to multiple equilibrium ones. Finally, we discuss the possibility of realizing an engine that works at unit efficiency by exploiting quantum coherence present in the reservoir.
In the present paper, quantum speed limit (QSL) time of a bipartite V-type three-level atomic system under the effect of two-qutrit entanglement is investigated. Each party interacts with own independent reservoir. By considering two local unitarily equivalent Wener states and the Horodecki PPT state, as initial states, the QSL time is evaluated for each of them in the respective entangled regions. It is counterintu-itively observe that the effect of entanglement on the QSL time driven from each of the initial Werner states are completely different when the degree of non-Markovianity is consid…
The dissipative dynamics of two interacting qubits coupled to independent reservoirs at nonzero temperatures is investigated, paying special attention to the entanglement evolution. The counter-rotating terms in the qubit-qubit interaction give rise to stationary entanglement, traceable back to the ground state structure. The robustness of this entanglement against thermal noise is thoroughly analyzed, establishing that it can be detected at reasonable experimental temperatures. Some effects linked to a possible reservoir asymmetry are brought to light.
We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.
We study the exact entanglement dynamics of two qubits interacting with a common zero-temperature non-Markovian reservoir. We consider the two qubits initially prepared in Bell-like states or extended Werner-like states. We study the dependence of the entanglement dynamics on both the degree of purity and the amount of entanglement of the initial state. We also explore the relation between the entanglement and the von Neumann entropy dynamics and find that these two quantities are correlated for initial Bell-like states.
Extending echo state property for quantum reservoir computing
本文针对传统回声状态性质无法刻画非平稳系统的问题，提出非平稳 ESP 和子空间/子集 ESP 两类新定义，并在量子储备池计算中通过 NARMA 任务和记忆容量分析验证其对应关系，为 QRC 及非平稳 RC 系统的实际设计提供新理解。
A pure-dephasing reservoir acting on an individual quantum system induces loss of coherence without energy exchange. When acting on composite quantum systems, dephasing reservoirs can lead to a radically different behavior. Transport of energy between two pure-dephasing markovian reservoirs is predicted in this work. They are connected through a chain of coupled sites. The baths are kept in thermal equilibrium at distinct temperatures. Quantum coherence between sites is generated in the steady-state regime and results in the underlying mechanism sustaining the effect. A quantum model for the r…
In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator interacting with a reservoir, we evaluate microscopically the condition under which the equilibration to a canonical state is valid. It is revealed that the non-Markovian effect and the availability of a stationary state of the total system play a profound role in the equilibration. In the Markovian limit, the conventional canonical state can be recovered. I…
We study the non-Markovian effect on the dynamics of the quantum discord by exactly solving a model consisting of two independent qubits subject to two zero-temperature non-Markovian reservoirs, respectively. Considering the two qubits initially prepared in Bell-like or extended Werner-like states, we show that there is no occurrence of the sudden death, but only instantaneous disappearance of the quantum discord at some time points, in comparison to the entanglement sudden death in the same range of the parameters of interest. It implies that the quantum discord is more useful than the entang…
Non-Markovian Dynamics in Fiber Delay-line Buffers
本研究针对双光子偏振纠缠态中存储于光纤延迟线缓冲器的光子，提出光子量子比特与光纤双折射及环境库耦合的模型，推导非马尔可夫概率函数并经量子态层析验证，发现系统处于非马尔可夫跃迁阈值略上方，且量子失协可突破Werner判据维持长时关联。
The generation of quantum entanglement of macroscopic or mesoscopic bodies in mechanical motion is generally bounded by the thermal fluctuation exerted by their environments. Here we propose a scheme to establish stationary entanglement between two mechanically oscillating mirrors of a cavity. It is revealed that, by applying a broadband squeezed laser acting as a squeezed-vacuum reservoir to the cavity, a stable entanglement between the mechanical mirrors can be generated. Using the adiabatic elimination and master equation methods, we analytically find that the generated entanglement is esse…
Ion chains are promising platforms for studying and simulating quantum reservoirs. One interesting feature is that their vibrational modes can mediate entanglement between two objects which are coupled through the vibrational modes of the chain. In this work we analyse entanglement between the transverse vibrations of two heavy impurity defects embedded in an ion chain, which is generated by the coupling with the chain vibrations. We verify general scaling properties of the defects dynamics and demonstrate that entanglement between the defects can be a stationary feature of these dynamics. We …
We study the dynamics of a macroscopic superconducting qubit coupled to two independent non-stationary reservoirs by using time-dependent perturbation theory. We show that an equilibrium environment surpasses the coherent evolution of the macroscopic qubit completely. When the qubit couples to two different reservoirs, exemplifying a non-equilibrium environment, the short-time dynamics is affected by the interference between two reservoirs, implying the non-additivity of effects of two reservoirs. The non-additivity can be traced back to a non-Markovian effect, even though two reservoirs are i…
We propose a mechanism to explain the nature of the damping of Rabi oscillations with increasing driving-pulse area in localized semiconductor systems, and have suggested a general approach which describes a coherently driven two-level system interacting with a dephasing reservoir. Present calculations show that the non-Markovian character of the reservoir leads to the dependence of the dephasing rate on the driving-field intensity, as observed experimentally. Moreover, we have shown that the damping of Rabi oscillations might occur as a result of different dephasing mechanisms for both statio…
We consider a three-level quantum system interacting with a bosonic thermal reservoir. Two energy levels of the system are nearly degenerate but well separated from the third one. The system-reservoir interaction constant is larger than the energy difference of the degenerate levels, but it is smaller than the separation between the latter and the remaining level. We show that the quasi-degeneracy of energy levels leads to the existence of a manifold of quasi-stationary states, and the dynamics exhibits two characteristic time scales. On the first, shorter one, initial states approach the quas…
We propose an effective approach for generating highly pure and strong cavity-mechanical entanglement (or optical-microwave entanglement) in a hybrid modulated three-mode optomechanical system. By applying two-tone driving to the cavity and modulating the coupling strength between two mechanical oscillators (or between a mechanical oscillator and a transmission line resonator), we obtain an effective Hamiltonian where an intermediate mechanical mode acting as an engineered reservoir cools the Bogoliubov modes of two target system modes via beam-splitter-like interactions. In this way, the two …
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the init…
We investigate the long-lived quantum coherence of two-level spontaneous emission models within structured environments. The population of the system under the asymptotic non-Markovian dynamics is linked to the spectral density of the reservoir through a general functional relation between them. We figure out explicitly the preservation of quantum coherence, via notions of entanglement and quantum discord, in connection with the spectral parameters of Ohmic class reservoirs and then show how to achieve them optimally. We expect these results to contribute towards reservoir engineering with the…
A procedure to obtain the dynamics of $N$ independent qudits ($d$-level systems) each interacting with its own reservoir, for any arbitrary initial state, is presented. This is then applied to study the dynamics of the entanglement of two qubits, initially in an extended Werner-like mixed state with each of them in a zero temperature non-Markovian environment. The dependence of the entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit e…
We investigate the exact dynamics of trace distance discord by considering two qubits under dephasing whose states belong to a class of $X$ states beyond Bell diagonal form. The necessary condition for the occurrence of freezing trace distance discord is found and compared with that of entropic discord. For an illustration, we consider two interacting qubits coupled to independent reservoirs and demonstrate these dynamical properties of trace distance discord. It is interesting to find that the freezing trace distance discord exists even for $X$ states without maximally mixed marginals and can…
Heat transfer in transversely coupled qubits: Optically controlled thermal modulator with common reservoirs
本文研究横向耦合量子比特与公共热库的热传递，发现公共热库通常抑制热流但在特定耗散条件下可增强热流，并利用暗态设计光控热调制器，同时揭示纠缠可作为调控热输运的资源。
This work addresses the problem of relaxation of open systems to quasi-equilibrium states. Time-dependent density matrix of two arbitrary coupled quantum oscillators of arbitrary properties interacting with separate reservoirs is derived based on path integration. Temporal dynamics of spatial variances and covariances of the oscillators from any given time up to quasi-equilibrium steady states is studied. It is demonstrated for general case that asymptotic spatial variances of two arbitrary oscillators and their covariances achieve stationary values in the long-time limit. A comparison of stea…
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak and strong coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of non-selective measurements can protect the relevant en…
We show how strong steady-state entanglement can be achieved in a three-mode optomechanical system (or other parametrically-coupled bosonic system) by using one of the modes as a cold reservoir to effectively laser-cool a delocalized Bogoliubov mode. This approach allows one to surpass the bound on the maximum stationary intracavity entanglement possible with a coherent two-mode squeezing interaction. Unlike typical dissipative entanglement schemes, the entangling dynamics here are most effective in a regime where the effects of the engineered reservoir cannot be described by a Markovian Lindb…
We propose schemes for generating spatially-separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage, or in the steady state with applied bias voltage. In both cases so-called Werner states with spin singlet fidelity exceeding 1/2 are generated, which indicates entanglement.
For a small system the coupling to a reservoir causes energy shifts as well as transitions between the system's energy levels. We show for a general stationary situation that the energy shifts can essentially be reduced to the relaxation rates. The effects of reservoir fluctuations and self reaction are treated separately. We apply the results to a two-level atom coupled to a reservoir which may be the vacuum of a radiation field.
Reservoir-conditioned virtual returns generate random Liouvillian skin localization in a reciprocal Mott insulator
本研究在互易莫特绝缘体中通过条件化虚拟回返实现随机刘维尔皮肤局域化，揭示了局部速率不平衡与多体稳态及慢弛豫的关联，为控制开放量子输运提供新途径。
Non-Markovian thermal reservoirs for autonomous entanglement distribution
本文提出一种利用非马尔可夫热浴生成两个分离量子比特间稳态纠缠的新方案，通过减少热源带宽使量子比特从分离态进入纠缠稳态，揭示了非马尔可夫性在量子通信中的应用。
We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, non-stationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time, and asymptotically drives the many-particle configuration into an equilibrium state where …
We investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrised by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the dynamical decoupling scheme, leading to a worse coherence preservation. We show that each …
In a bipartite system subject to decoherence from two separate reservoirs, the entanglement is typically destroyed faster than for single reservoirs. Surprisingly however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends up in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on t…
From quantum mechanical first principles only, we rigorously study the time-evolution of a $N$-level atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at thermal equilibrium (reservoir). In particular, we establish the relation between the full dynamics of the compound system and the effective dynamics for the $N$-level atom, which is studied in detail in [Bru-de Siqueira Pedra-Westrich, Annales Henri Poincaré, 13(6):1305-1370, 2012]. Together with [Bru-de Siqueira Pedra-Westrich, Annales Henri Poincaré, 13(6):1305-1370, 2012] t…
Multi-mode entanglement is investigated in the system composed of $N$ coupled identical harmonic oscillators interacting with a common environment. We treat the problem very general by working with the Hamiltonian without the rotating-wave approximation and by considering the environment as a non-Markovian reservoir to the oscillators. We invoke an $N$-mode unitary transformation of the position and momentum operators and find that in the transformed basis the system is represented by a set of independent harmonic oscillators with only one of them coupled to the environment. Working in the Wig…
The paper deals with the problem of open systems out of equilibrium. An analytical expression for time-dependent density matrix of two arbitrary coupled identical quantum oscillators interacting with separate reservoirs is derived using path integral methods. The temporal behavior of spatial variances and of covariance from given initial values up to stationary values is investigated. It was shown that at comparatively low coupling strengths the asymptotic variances in the long-time limit achieve steady states despite on initial conditions. Stationary values of variances differ from the case o…
Enhanced Quantum Mpemba Effect with Squeezed Thermal Reservoirs
本文通过开放量子系统动力学给出量子姆潘巴效应的充分条件，并引入姆潘巴参数量化效应强度，进而利用压缩热库的非经典特性实现增强的量子姆潘巴效应。
Thermodynamic incompleteness of state dynamics in Markovian transport
研究揭示了马尔可夫传输中状态动力学的热力学不完整性，指出即使状态主方程固定了occupation概率、稳态响应和弛豫，仍需明确底层跃迁如何分配到库和能量滤波器。
Reservoir engineering lattice states using only localized engineered dissipation is extremely attractive from a resource point of view, but can suffer from long relaxation times. Here, we study the relaxation dynamics of bosonic lattice systems locally coupled to a single squeezed reservoir. Such systems can relax into a highly non-trivial pure states with long-range entanglement. In the limit of large system size, analytic expressions for the dissipation spectrum can be found by making an analogy to scattering from a localized impurity. This allows us to study the cross-over from perturbative…
We deduce a class of non-Markovian completely positive master equations which describe a system in a composite bipartite environment, consisting of a Markovian reservoir and additional stationary unobserved degrees of freedom that modulate the dissipative coupling. The entanglement-induced memory effects can persist for arbitrary long times and affect the relaxation to equilibrium, as well as induce corrections to the quantum-regression theorem. By considering the extra degrees of freedom as a discrete manifold of energy levels, strong non-exponential behavior can arise, as for example power l…
Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital computers. An emerging scheme is reservoir computing which exploits nonlinear dynamical systems for temporal information processing. This paper introduces reservoir computers with output feedback as stationary and ergodic infinite-order nonlinear autoregressive models. We highlight the versatility of this approach by employing classical and quantum reservoir computer…
An experimental demonstration of a non-classical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary oscillator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5 - 0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$ and for support temperatures of T $\approx$ 25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed st…
Magnon squeezing via reservoir-engineered optomagnomechanics
本文提出在光磁力力学系统中通过光学腔双音驱动产生机械压缩并传递至磁振子模式，在线性和色散耦合下分别实现稳态与瞬态磁振子压缩态，可用于量子信息处理和量子传感。
Entangling remote qubits through a two-mode squeezed reservoir
本研究展示了一种通过量子关联光子库自主纠缠远程超导量子比特的新方法，并利用该平台直接认证双模压缩，为量子网络提供了新平台。
Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir
本文严格证明光学模式经分束器序列与非平衡库散射后，在特定条件下趋于热平衡，且纯态时与库最大纠缠、非经典性降低。
A finite quantum system S is coupled to a thermal, bosonic reservoir R. Initial SR states are possibly correlated, obtained by applying a quantum operation taken from a large class, to the uncoupled equilibrium state. We show that the full system-reservoir dynamics is given by a markovian term plus a correlation term, plus a remainder small in the coupling constant $λ$ uniformly for all times $t\ge 0$. The correlation term decays polynomially in time, at a speed independent of $λ$. After this, the markovian term becomes dominant, where the system evolves according to the completely positive, t…
We consider an impurity ($N$--level atom) driven by monochromatic light in a host environment which is a fermionic thermal reservoir. The external light source is a time--periodic perturbation of the atomic Hamiltonian stimulating transitions between two atomic energy levels $E_{1}$ and $E_{N}$ and thus acts as an optical pump. The purpose of the present work is the analysis of the effective atomic dynamics resulting from the full microscopic time--evolution of the compound system. We prove, in particular, that the atomic dynamics of population relaxes for large times to a quasi-stationary sta…
We develop a framework to analyze the dynamics of a finite-dimensional quantum system $\rm S$ in contact with a reservoir $\rm R$. The full, interacting $\rm SR$ dynamics is unitary. The reservoir has a stationary state but otherwise dissipative dynamics. We identify a main part of the full dynamics, which approximates it for small values of the $\rm SR$ coupling constant, uniformly for all times $t\ge 0$. The main part consists of explicit oscillating and decaying parts. We show that the reduced system evolution is Markovian for all times. The technical novelty is a detailed analysis of the l…
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