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 relaxation to a slow, quantum-Zeno regime. We also find the possibility of regimes of accelerated relaxation due to a surprising impedance matching phenomena. We also study intermediate time behaviors, identifying a long-lived "prethermalized" state associated that exists within a light cone like area. This intermediate state can be quasi-stationary, and can very different entanglement properties from the ultimate dissipative steady state.
We study how the thermalization time of a single radiation cavity-field mode changes drastically depending on the type of the atomic reservoir it interacts. Temporal evolution of the field is analyzed within the micromaser scheme, where each atomic reservoir is modeled as a beam of atoms crossing an electromagnetic cavity in which they weakly interact with the field. The cavity-field thermalizes when we consider either multi-atom or multi-level atom reservoirs. We found that each atomic reservoir generates a different scaling law in the thermalization time of the cavity-field. Such scaling law…
In this paper, we study the exact dynamics of general open systems interacting with its environment through particle exchanges. The paper includes two main results. First, by taking advantage of the propagating function in the coherent state representation, we solve the exact master equation, whose solution is expressed in terms of the Keldysh nonequilibrium Green functions. Second, in the dynamical perspective, we provide a rigorous thermalization process of open quantum systems.
We study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that are individually coupled to non-Markovian reservoirs. This coupling ensures that the dynamical equations of the atoms can be treated independently. The non-Markovian reservoirs are described by a model which leads to an exact non-Markovian master equation of the Nakajima-Zwanzig form [J. Salo, S. M. Barnett, and S. Stenholm, Optics Commun. 259, 772 (2006)]. We consider the evolution of the entanglement of a two-atom state that is initially completely entangled, quantified by its …
We show how a generalized kind of chiral symmetry can be used to construct highly-efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension, and does not rely on translational invariance. We show how the relevant symmetry operation directly determines the real space correlation structure in the steady state, and give several examples that are within reach in sever…
We illustrate scenarios in which Hawking radiation collected in finite regions of a reservoir provides temporary access to the interior of black holes through transient entanglement "islands". Whether these islands appear and the amount of time for which they dominate - sometimes giving way to a thermalization transition - is controlled by the amount of radiation we probe. In the first scenario, two reservoirs are coupled to an eternal black hole. The second scenario involves two holographic quantum gravitating systems at different temperatures interacting through a Rindler-like reservoir, whi…
Closed quantum systems exhibit different dynamical regimes, like Many-Body Localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition for the s…
We study the thermalization of a small $XX$ chain coupled to long, gapped $XXZ$ leads at either side by observing the relaxation dynamics of the whole system. Using extensive tensor network simulations, we show that such systems, although not integrable, appear to show either extremely slow thermalization or even lack thereof since the two can not be distinguished within the accuracy of our numerics. We show that the persistent oscillations observed in the spin current in the middle of the $XX$ chain are related to eigenstates of the entire system located within the gap of the boundary chains.…
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on the relaxation dynamics of observables as described by the diagonal part of ETH, whose verification requires substantial numerical input. This leaves many of the general assumptions of ETH untested. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations, which directly probe the off-diagonal part of ETH…
The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well-approximate thermal states. A quantum optical scheme for the laboratory ass…
Encoding complex-balanced thermalization in quantum circuits
Zhejiang University（浙江大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Harbin Institute of Technology（哈尔滨工业大学）；Institute for Advanced Studies of Physics, Zhejiang University（浙江大学高等研究院）；Beijing Normal University（北京师范大学）
We explore the electromagnetic field coupled to a mechanical resonator via quadratic optomechanical interaction in the reversed dissipation regime where the mechanical damping rate is much larger than the cavity field dissipation rate. It is shown that in this regime, the cavity field effectively acquires an additional reservoir which is conditioned by the temperature of the mechanical bath as well as the mechanical damping rate. We analytically find the steady-state mean photon number and the critical temperature of the mechanical oscillator to cool or heat the coupled electromagnetic field. …
We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs of free massless bosonic fields. We apply our general results to the specific case of the qubit. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.
We investigate a `pseudo thermalization' effect, where an open quantum system coupled to several non-Markovian reservoirs presents an emergent thermal behaviour in spite of its coupling to a non-equilibrated environment. The thermal behaviour is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a mic…
The sensitivity of entanglement to the thermal and squeezed reservoirs' parameters is investigated regarding entanglement decay and what is called sudden-death of entanglement, ESD, for a system of two qubit pairs. The dynamics of information is investigated by means of the information disturbance and exchange information. We show that for squeezed reservoir, we can keep both of the entanglement and information survival for a long time. The sudden death of information is seen in the case of thermal reservoir.
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.
Isolation of a system from its environment is often desirable, from precision measurements to control of individual quantum systems; however, dissipation can also be a useful resource. Remarkably, engineered dissipation enables the preparation of quantum states of atoms, ions or superconducting qubits as well as their stabilization. This is achieved by a suitably engineered coupling to a dissipative cold reservoir formed by electromagnetic modes. Similarly, in the field of cavity electro- and optomechanics, the control over mechanical oscillators utilizes the inherently cold, dissipative natur…
Dynamic correlation and response functions of classical and quantum systems in thermal equilibrium are connected by fluctuation-dissipation theorems, which allow an alternative definition of their (unique) temperature. Motivated by this fundamental property, we revisit the issue of thermalization of closed many-body quantum systems long after a sudden quench, focussing on the non-equilibrium dynamics of the Ising chain in a critical transverse field. We show the emergence of distinct observable-dependent effective temperatures, which rule out Gibbs thermalization in a strict sense but might st…
We have investigated theoretically a dissipative polariton system in the ultrastrong light-matter coupling regime without using the rotating-wave approximation on system-reservoir coupling. Photons in a cavity and excitations in matter respectively couple two large ensembles of harmonic oscillators (photonic and excitonic reservoirs). Inheriting the quantum statistics of polaritons in the ultrastrong coupling regime, in the ground state of the whole system, the two reservoirs are not in the vacuum states but they are squeezed and correlated. We suppose this non-vacuum reservoir state in the ma…
The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian …
In vibrational strong coupling (VSC), molecular vibrations strongly interact with the modes of an optical cavity to form hybrid light-matter states known as vibrational polaritons. Experiments show that the kinetics of thermally activated chemical reactions can be modified by VSC. Transition-state theory, which assumes that internal thermalization is fast compared to reactive transitions, has been unable to explain the observed findings. Here, we carry out kinetic simulations to understand how dissipative processes, namely those that VSC introduces to the chemical system, affect reactions wher…
Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources both in quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average ph…
We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasi…
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlightin…
In a recent work, we have derived simple Lindblad-based equations for the thermalization of systems in contact with a thermal reservoir. Here, we apply these equations to the Lipkin-Meshkov-Glick model (LMG) in contact with a blackbody radiation and analyze the dipole matrix elements involved in the thermalization process. We find that the thermalization can be complete only if the density is sufficiently high, while, in the limit of low density, the system thermalizes partially, namely, within the Hilbert subspaces where the total spin has a fixed value. In this regime, and in the isotropic c…
Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer's framework if they rely on an interaction between the object and a thermal reservoir. Landauer's principle dictates that this must dissipate a minimum quantity of heat, proportional to the entropy reduction that is incurred by the object, to the thermal reservoir. However, this lower bound is only reachable for some specific physical situations, and it is not necessarily achievable for any given reser…
Ancilla mediated steady-state engineering in open quantum systems
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；University of Potsdam, Institute of Physics and Astronomy（波茨坦大学物理与天文学研究所）；Raman Research Institute（拉曼研究所）；Department of Physics and Astronomy, University of Exeter（埃克塞特大学物理与天文学系）
The generation of entanglement between two oscillators that interact via a common reservoir is theoretically studied. The reservoir is modeled by a one-dimensional harmonic crystal initially in thermal equilibrium. Starting from a separable state, the oscillators can become entangled after a transient time, that is of the order of the thermalization time scale. This behavior is observed at finite temperature even when the oscillators are at a distance significantly larger than the crystal's interparticle spacing. The underlying physical mechanisms can be explained by the dynamical properties o…
The quantum dynamics of a two state system coupled to a bosonic reservoir with sub-Ohmic spectral density is investigated for strong friction. Numerically exact path integral Monte Carlo methods reveal that in contrast to conventional expectations, coherent dynamics never turns into incoherent decay for a broad class of spectral distributions. Coherences associated with substantial system-reservoir entanglement exist in non-equilibrium even when strong dissipation makes the thermodynamic state of the system to behave essentially classical. This may be of relevance for current experiments with …
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir.
Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir. Generically, in this operation the external agent performs work onto the system, preventing thermalization when the reservoir is at equilibrium. One can recover thermalization by considering an autonomous global setup where the reservoir particles colliding with the system possess a kinetic degree of freedom. The drawback is that the corresponding scattering p…
Dissipation engineering is a powerful framework for quantum state preparation and autonomous error correction in few-qubit systems. In this work, we examine the scalability of this approach and give three criteria which any dissipative state stabilization protocol should satisfy to be truly scalable as the number of qubits grows. Besides the requirement that it can be constructed in a resource-efficient manner from simple-to-engineer building blocks, a scalable protocol must also exhibit favorable scaling of the stabilization time with the increase in system size. We present a family of protoc…
The Brownian motion of a single particle is a paradigmatic model of the nonequilibrium dynamics of dissipative systems. In the system-plus-reservoir approach, one can derive the particle's equations of motion from the reversible dynamics of the system coupled to a bath of oscillators representing its thermal environment. However, extending the system-plus-reservoir approach to multiple particles in a collective environment is not straightforward, and conflicting models have been proposed to that end. Here, we set out to reconcile some aspects of the nonlinear and the bilinear models of two Bro…
We demonstrate how a time-dependent dissipative environment may be used as a tool for controlling the quantum state of a two-level atom. In our model system the frequency and coupling strength associated with microscopic reservoir modes are modulated, while the principal features of the reservoir structure remain fixed in time. Physically, this may be achieved by containing a static atom-cavity system inside an oscillating external bath. We show that it is possible to dynamically decouple the atom from its environment, despite the fact that the two remain resonant at all times. This can lead t…
The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature is studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics is completely determined by the propagating (retarded) and correlation Green functions. Compare the non-Markovian behavior at finite temperature with those at zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory eff…
Reservoir-independent lossless charging and protected storage of an open quantum battery
Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（卡塔尔量子计算中心，科学与工程学院，哈马德·本·哈利法大学）；The University of Adelaide（阿德莱德大学）
