When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We formulate a theory which fully accounts for the associated, distinct time scales, and identifies the parameter dependence of the decay rate which ultimately controls the convergence towards equilibrium. Our formalism guarantees total particle number conservation and fundamental consistency between macroscopic and internal currents flowing in the system. We furthermore establish a clear imprint of the fermionic or bosonic particle character on the resulting conductance.
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…
The breaking of reciprocity is a topic of great interest in fundamental physics and optical information processing applications. We demonstrate non-reciprocal light transport in a quantum system of hot atoms by engineering the dissipative atomic reservoir. Our scheme is based on the phase-sensitive light transport in a multi-channel photon-atom interaction configuration, where the phase of collective atomic excitations is tunable through external driving fields. Remarkably, we observe inter-channel quantum correlations which originate from interactions with the judiciously engineered reservoir…
We investigate the heat transport between two nonthermal reservoirs based on a microscopic collision model. We consider a bipartite system consisting of two identical subsystems, and each subsystem interacts with its own local reservoir, which consists of a large collection of initially uncorrelated ancillas. Then a heat transport is formed between two reservoirs by a sequence of pairwise collisions (inter-subsystem and subsystem-local reservoir). In this paper we consider two kinds of reservoir's initial states, the thermal state, and the state with coherence whose diagonal elements are the s…
A unified diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model
We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.
We analyze quantum state of fermionic carriers in a transport channel attached to a particle reservoir. The analysis is done from the first principles by considering microscopic models of the reservoir and transport channel. In the case of infinite effective temperature of the reservoir we demonstrate a full agreement between the results of straightforward numerical simulations of the system dynamics and solution of the specified master equation on the single-particle density matrix of the carriers in the channel. This allows us to predict the quantum state of carriers in the case where transp…
Clausius' statement of the second law of thermodynamics reads: Heat will flow spontaneously from a hot to cold reservoir. This statement should hold for transport of energy through a quantum network composed of small subsystems each coupled to a heat reservoir. When the coupling between nodes is small, it seems reasonable to construct a local master equation for each node in contact with the local reservoir. The energy transport through the network is evaluated by calculating the energy flux after the individual nodes are coupled. We show by analysing the most simple network composed of two qu…
Quantum transport along a tight-binding chain connected to Markovian reservoirs
Kirensky Institute of Physics, Federal Research Centre KSC SB RAS（基连斯基物理研究所，俄罗斯科学院西伯利亚分院克拉斯诺亚尔斯克科学中心联邦研究中心）；IRC SQC, Siberian Federal University（西伯利亚联邦大学量子系统与量子控制国际研究中心）；School of Engineering Physics and Radio Electronics, Siberian Federal University（西伯利亚联邦大学工程物理与无线电电子学院）
We analyze the current of Bose particles across the tight-binding chain connected at both ends to the particles reservoirs. Unlike the standard open Bose-Hubbard model, where the presence of reservoirs is taken into account by the Lindbladians acting on the first and the last sites of the chain, we use the semi-microscopic models for the reservoirs. This allows us to address the case of arbitrary reservoir temperature. In particular, we discuss the phenomenon of the resonant transmission for nearly condensed bosons, where the current across the chain is significantly enhanced for certain value…
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 …
In this paper, based on the notion of pseudomode framework introduced by Garraway in [Phys. Rev. A 55, 2290 (1997)], we propose a mechanism for enhancing the efficiency of excitation energy transport in a spin channel which is in contact with a Lorentzian reservoir, through the inclusion of other similar auxiliary spin chains into the reservoir. To this aim, a Lindblad-type master equation for the dynamics of the transport process is provided on the basis of pseudomode approach. It is figured out that increasing the number of auxiliary chains in the reservoir enhances the efficiency of transpo…
We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite temperature engineered reservoirs can lead to the experimental observation of thermal entanglement --the appearance and increase of entanglement with temperature-- to the study of the dependence of finite time disentanglement and revival with temperature, quantum thermodynamical effects, among many other applications, enlarging the comprehension of te…
We investigate decoherence-free evolution (DFE) of quantum discord (QD) for two initially-correlated qubits in two finite-temperature reservoirs using an exactly solvable model. We study QD dynamics of the two qubits coupled to two independent Ohmic reservoirs when the two qubits are initially prepared in X-type quantum states. It is found that reservoir temperature significantly affects the DFE dynamics. We show that it is possible to control the DFE and to prolong the DFE time by choosing suitable parameters of the two-qubit system and reservoirs.
We explore the effects of quantum mechanical squeezing on the nonequilibrium fluctuations of bosonic transport between two squeezed harmonic reservoirs and a two level system. A standard full counting statistics technique based on a quantum master equation is employed. We derive a nonzero thermodynamic affinity under equal temperature setting of the two squeezed reservoirs. The odd cumulants are shown to be independent of squeezing under symmetric conditions, whereas the even cumulants depend nonlinearly on the squeezing parameters. The odd and even cumulants saturate at two different but uniq…
The geometric phase is of fundamental interest and plays an important role in quantum information processing. However, the definition and calculation of this phase for open systems remains a problem due to the lack of agreement on generalizations of the parallel transport condition to mixed state nonunity evolutions. Here we tackle this problem by associating the open system geometric phase with the parallel transport of the joint system-reservoir state. Our approach not only provides a way around the nonunitary evolution obstacle, but also sheds light on the relation between the geometric pha…
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. C…
A general formalism for computing the full counting statistics of energy exchanged between 'N' squeezed thermal photon reservoirs weakly coupled to a cavity with 'M' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases, the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time statistics is signifi…
We describe a scheme for entangling mechanical resonators which is efficient also beyond the resolved sideband regime. It employs the radiation pressure force of the squeezed light produced by a degenerate optical parametric oscillator, which acts as a reservoir of quantum correlations (squeezed reservoir), and it is effective when the spectral bandwidth of the reservoir and the fields frequencies are appropriately selected. It allows for the steady state preparation of mechanical resonatrs in entangled EPR states and can be extended to the preparation of many entangled pairs of resonators whi…
We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of non-interacting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.
We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum cor…
We propose a method for directly probing the dynamics of disentanglement of an initial two-qubit entangled state, under the action of a reservoir. We show that it is possible to detect disentanglement, for experimentally realizable examples of decaying systems, through the measurement of a single observable, which is invariant throughout the decay. The systems under consideration may lead to either finite-time or asymptotic disentanglement. A general prescription for measuring this observable, which yields an operational meaning to entanglement measures, is proposed, and exemplified for cavity…
We investigate the dynamical properties of the finite-size Dicke model coupled to a photon reservoir in the dispersive regime. The system-reservoir coupling in our Hamiltonian includes counter-rotating terms, which are relevant in the strong atom-cavity coupling. Because the dispersive regime is considered, the dynamics of low-energy states are described sufficiently accurately within the finite-dimensional subspace of the dressed states. Using the separation of the time scales between the system and the reservoir, we derive the Markovian quantum master equation in the subspace without ignorin…
Cross-Spectral Reservoir Correlations as a Resource for Finite-Time Quantum Otto Engines
Ramakrishna Mission Vivekananda Educational and Research Institute（拉马克里希纳使命维韦卡南达教育研究所）；TCG CREST；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）
By using the effective non-Markovian measure [H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local reservoir. We show that subsystem dynamics can be controlled by manipulating the coupling between TLAs, temperature and relaxation rate of the atoms. Moreover, the correlation between non-Markovianity of subsystem and entanglement between the subsystem and the structured bath is investigated, the results show that the emergence of non-Markovianity has a nega…
Reservoir engineering is a powerful tool for the robust generation of quantum states or transport properties. Using both a weak-coupling quantum master equation and the exact solution, we show that directional transport of electrons through a double quantum dot can be achieved through an appropriately designed electronic environment. Directionality is attained through the interference of coherent and dissipative coupling. The relative phase is tuned with an external magnetic field, such that directionality can be reversed, as well as turned on and off dynamically. Our work introduces fermionic…
We show how Cooper-pair-assisted transport, which describes the stimulated transport of electrons in the presence of Cooper-pairs, can be engineered and controlled with cold atoms, in regimes that are difficult to access for condensed matter systems. Our model is a channel connecting two cold atomic gases, and the mechanism to generate such a transport relies on the coupling of the channel to a molecular BEC, with diatomic molecules of fermionic atoms. Our results are obtained using a Floquet-Redfield master equation that accounts for an exact treatment of the interaction between atoms in the …
We consider thermal transport between two reservoirs coupled by a quantum Ising chain as a model for non-equilibrium physics induced in quantum-critical many-body systems. By deriving rate equations based on exact expressions for the quasiparticle pairs generated during the transport, we observe signatures of the underlying quantum phase transition in the steady-state energy current already at finite reservoir temperatures.
A ballistic atom pump is a system containing two reservoirs of neutral atoms or molecules and a junction connecting them containing a localized time-varying potential. Atoms move through the pump as independent particles. Under certain conditions, these pumps can create net transport of atoms from one reservoir to the other. While such systems are sometimes called "quantum pumps," they are also models of classical chaotic transport, and their quantum behavior cannot be understood without study of the corresponding classical behavior. Here we examine classically such a pump's effect on energy a…
We present a generic, compact formula for the current flowing in interacting and non-interacting systems which are driven out-of-equilibrium by biased reservoirs described by Lindblad jump operators. We show that, in the limit of high temperature and chemical potential, our formula is equivalent to the well-known Meir-Wingreen formula, which describes the current flowing through a system connected to fermionic baths, therefore bridging the gap between the two formalisms. Our formulation gives a systematic way to address the transport properties of correlated systems strongly driven out of equi…
Long-time fermionic quantum transport with controlled full-state error using an adaptive reservoir-mode window
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Faculty of Physics, M.V.Lomonosov Moscow State University（莫斯科国立大学物理系）；National Research Nuclear University MEPhI（莫斯科工程物理学院）
An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of quantum reservoirs coupled to regions where the system is described by nonlinear ordinary differential equations and has a general conceptual interest.
We study particle current and occupation distribution in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (mesoreservoir) is driven out of equilibrium by the action of superreservoirs with prescribed temperatures and chemical potentials described by a simple dissipative mechanism with the Lindblad equation. We compare exact (numerical) results for the non-equilibrium steady state particle current with theoretical expectations based on the Landauer formula and show that the model reproduce the behavior of coherent quantum …
Landauer's erasure principle puts a fundamental constraint on the amount of work required to erase information using thermal reservoirs. Recently this bound was improved to include corrections for finite-sized thermal reservoirs. In conventional information-erasure schemes, conservation of energy plays a key role with the cost of erasure. However, it has been shown that erasure can be achieved through the manipulation of spin angular momentum rather than energy, using a reservoir composed of energy-degenerate spin particles under the constraint of the conservation of spin angular momentum, in …
We study heat current and the full statistics of heat fluctuations in a capacitively-coupled double quantum dot system. This work is motivated by recent theoretical studies and experimental works on heat currents in quantum dot circuits. As expected intuitively, within the (static) mean-field approximation, the system at steady-state decouples into two single-dot equilibrium systems with renormalized dot energies, leading to zero average heat flux and fluctuations. This reveals that dynamic correlations induced between electrons on the dots is solely responsible for the heat transport between …
The pursuit of the non-Hermitian skin effect (NHSE) in various physical systems is of great research interest. Compared with recent progress in non-electronic systems, the implementation of the NHSE in condensed matter physics remains elusive. Here, we show that the NHSE can be engineered in the mesoscopic heterojunctions (system plus reservoir) in which electrons in two channels of the system moving towards each other have asymmetric coupling to those of the reservoir. This makes electrons in the system moving forward and in the opposite direction have unequal lifetimes, and so gives rise to …
When two chains of quantum systems are driven at their ends by a two-mode squeezed reservoir, they approach a steady state characterized by the formation of many entangled pairs. Each pair is made of one element of the first and one of the second chain. This effect has been already predicted under the assumption of broadband squeezing. Here we investigate the situation of finite-bandwidth reservoirs. This is done by modeling the driving bath as the output field of a non-degenerate parametric oscillator. The resulting non-Markovian dynamics is studied within the theoretical framework of cascade…
We study the non-equilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time $τ$ is bounded from below by the entropy production $σ_{\mathrm{min}}\propto1/τ$. We discover a general power-efficiency trade-off depending on the ratio of heat capacities ($γ$) of the reservoirs for the engine. And a universal efficiency at maximum average power of the engine for arbitrary $γ$ is obtained. For practical purposes, the operation p…
We show that finite system-reservoir coupling imposes a distinct quantum limit on the performance of a non-equilibrium quantum heat engine. Even in the absence of quantum friction along the isentropic strokes, finite system-reservoir coupling induces correlations that result in the generation of coherence between the energy eigenstates of the working system. This coherence acts to hamper the engine's power output, as well as the efficiency with which it can convert heat into useful work, and cannot be captured by a standard Born-Markov analysis of the system-reservoir interactions.
We construct a dissipation induced quantum transport scheme by coupling a finite lattice of $N$ two-level systems to an environment with a discrete number of energy levels. With the environment acting as a reservoir of energy excitations, we show that the coupling between the system and the environment gives rise to a mechanism for excited states of the system to be efficiently transported from one end of the lattice to another. We also show that we can adjust the efficiency of the quantum transport scheme by varying the spacing between energy levels of the system, by decreasing the ground sta…
We study the effect of system reservoir coupling on currents flowing through quantum junctions. We consider two simple double-quantum dot configurations coupled to two external fermionic reservoirs and study the net current flowing between the two reservoirs. The net current is partitioned into currents carried by the eigenstates of the system and by the coherences between the eigenstates induced due to coupling with the reservoirs. We find that current carried by populations is always positive whereas current carried by coherences are negative for large couplings. This results in a non-monoto…
Tunneling Dynamics and Time Delay in Electron Transport through Time-Dependent Barriers with Finite-Bandwidth Reservoirs
Weizmann Institute（魏茨曼科学研究所）；BCAM - Basque Center for Applied Mathematics（巴斯克应用数学中心）；Departmento de Química-Física, Universidad del País Vasco, UPV/EHU（巴斯克大学物理化学系）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克科学基金会）
Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics
Imperial College London（伦敦帝国理工学院）；City St George’s, University of London（伦敦大学城市圣乔治学院）；The Alan Turing Institute（艾伦·图灵研究所）；Politecnico di Torino（都灵理工大学）
Entropy Transport in Programmable Quantum Junctions
Peter Grünberg Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich（于利希研究中心）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学）
In this paper we investigate the spin currents and the von Neumann entropy (VNE) of an Heisenberg XXZ chain in contact with twisted XY-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the VNE. As a result we show that the maximal spin current always occurs in the proximity of extrema of the VNE and for particular choices…
