Strong disorder inhibits thermalization in isolated quantum systems and may lead to many-body localization (MBL). In realistic situations, however, the observation of MBL is hindered by residual couplings of the system to an environment, which acts as a bath and pushes the system to thermal equilibrium. This paper is concerned with the transient dynamics prior to thermalization and studies how the relaxation of a disordered system is altered under the influence of external driving and dissipation. We consider a scenario where a disordered quantum spin chain is placed into a strong magnetic field that polarizes the system. By suddenly removing the external field, a nonequilibrium situation is induced and the decay of magnetization probes the degree of localization. We show that by driving the system with light, one can distinguish between different dynamical regimes as the spins are more or less susceptible to the drive depending on the strength of the disorder. We provide evidence that some of these signatures remain observable at intermediate time scales even when the spin chain is subject to noise due to coupling to an environment. From a numerical point of view, we demonstrate that the open-system dynamics starting from a class of experimentally relevant mixed initial states can be efficiently simulated by combining dynamical quantum typicality with stochastic unraveling of Lindblad master equations.
Strong disorder inhibits thermalization in isolated quantum systems and may lead to many-body localization (MBL). In realistic situations, however, the observation of MBL is hindered by residual couplings of the system to an environment, which acts as a bath and pushes the system to thermal equilibrium. This paper is concerned with the transient dynamics prior to thermalization and studies how the relaxation of a disordered system is altered under the influence of external driving and dissipation. We consider a scenario where a disordered quantum spin chain is placed into a strong magnetic field that polarizes the system. By suddenly removing the external field, a nonequilibrium situation is induced and the decay of magnetization probes the degree of localization. We show that by driving the system with light, one can distinguish between different dynamical regimes as the spins are more or less susceptible to the drive depending on the strength of the disorder. We provide evidence that some of these signatures remain observable at intermediate time scales even when the spin chain is subject to noise due to coupling to an environment. From a numerical point of view, we demonstrate that the open-system dynamics starting from a class of experimentally relevant mixed initial states can be efficiently simulated by combining dynamical quantum typicality with stochastic unraveling of Lindblad master equations.
It is known that strong disorder in closed quantum systems leads to many-body localization (MBL), and that this quantum phase can be destroyed by coupling to an infinitely large Markovian environment. However, the stability of the MBL phase is less clear when the system and environment are of finite and comparable size. Here, we study the stability and eventual localization properties of a disordered Heisenberg spin chain coupled to a finite environment, and extensively explore the effects of environment disorder, geometry, initial state, and system-bath coupling strength, using the steady-state value of magnetization as a probe. Focusing on nonequilibrium dynamics and steady-state properties, our results indicate that within system sizes amenable to exact diagonalization, a strongly localized system interacting in a junction configuration retains remnant information on its initial state at long times despite coupling to a finite ergodic environment. In contrast, in a ladder configuration, strong dependencies on the initial state and coupling strength are observed, which can lead to either the loss or retention of information. Finally, we highlight and discuss discrepancies that can arise when similar methodologies are employed to infer localization or thermalization, revealing the need for careful interpretation.
Understanding how closed quantum systems dynamically approach thermal equilibrium presents a major unresolved problem in statistical physics. Generically, non-integrable quantum systems are expected to thermalize as they comply with the Eigenstate Thermalization Hypothesis. However, in the presence of strong disorder, the dynamics can possibly slow down to a degree that systems fail to thermalize on experimentally accessible timescales, as in spin glasses or many-body localized systems. In general, particularly in long-range interacting quantum systems, the specific nature of the disorder necessary for the emergence of a prethermal, metastable state--distinctly separating the timescales of initial relaxation and subsequent slow thermalization--remains an open question. We study an ensemble of Heisenberg spins with a tunable distribution of random coupling strengths realized by a Rydberg quantum simulator. We observe a drastic change in the late-time magnetization when increasing disorder strength. The data is well described by models based on pairs of strongly interacting spins, which are treated as thermal for weak disorder and isolated for strong disorder. Our results indicate a crossover into a pair-localized prethermal regime in a closed quantum system of thousands of spins in the critical case where the exponent of the power law interaction matches the spatial dimension.
Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.
When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.
Many-body localization, which prevents a many-body quantum systems from reaching thermal equilibrium has opened the possibility to study out-of-equilibrium dynamics of isolated quantum systems, leading to new phases of matter such as the discrete time crystal. However, little is known about these effects when the quantum many-body system is coupled to an external environment. An intuitive assumption is that out-of-equilibrium dynamics and quantum coherences would not survive due to thermalization with external degrees of freedom. The present work focuses on open quantum many-body systems and aims at the question how an external reservoir can preserve such out-of-equilibrium effects. In the first part, common generic reservoirs are assumed to focus on many-body effects of the systems of interest. As a first many-body system, an optically driven many-emitter phonon laser is investigated. The full quantum mechanical treatment reveals additional resonances caused by collective effects of the many-emitter setup. Optically addressing these resonances results in an enhancement of phonon intensities within the acoustic cavity. The Heisenberg spin-chain has achieved the role of a standard model to study many-body localization. As a second many-body system, the model is generalized to an open quantum system via boundary reservoirs which are driving the system out-of equilibrium and a spin-current is induced. When driven far from equilibrium, the transport is very much dependent on the external reservoirs. In contrast, it is demonstrated that a setup with long-range coupling between the spins shows transport behavior independent of the external environment. In the second part of this work, the coupling to the reservoir is structured by assuming a boundary condition. Experimentally this is achieved by placing a distant mirror close to the system. A common Born-Markov approximation leading to factorizing system and reservoir states is insufficient to describe these feedback dynamics. In this work, an approach is used to treat the reservoir states as part of the many-body system which is based on matrix product states using the quantum stochastic Schrödinger equation. Focusing on the reservoir statistics of a single two-level system, it is demonstrated that by combining time-dependent optical excitation with time-delayed feedback via structuring the reservoir, individual photon probabilities are controlled by changing external degrees of freedom. Finally, this method is generalized to a many-body system including a coupling to an external reservoir beyond Born-Markov approximation. It is shown that feedback dynamics stabilize a discrete time crystal against dissipation to the environment. Out-of-equilibrium dynamics and many-body localization of the discrete time crystal survive for long times even in the presence of an external environment and become independent of the coupling to the reservoir. The developed method benefits from small entanglement entropy of the many-body localized system as well as from a suppression of entanglement between system and reservoir due to the feedback dynamics. This allows to consider up to forty spins with individual structured reservoirs in a numerically exact manner.
We use an external spin as a dynamical probe of many-body localization. The probe spin is coupled to an interacting and disordered environment described by a Heisenberg spin chain in a random field. The spin-chain environment can be tuned between a thermalizing delocalized phase and nonthermalizing localized phase, both in its ground and high-energy states. We study the decoherence of the probe spin when it couples to the environment prepared in three states: the ground state, the infinite temperature state, and a high-energy N\'eel state. In the nonthermalizing many-body localized regime, the coherence shows scaling behavior in the disorder strength. The long-time dynamics of the probe spin shows a logarithmic dephasing in analogy with the logarithmic growth of entanglement entropy for a bipartition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization.