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arXiv:1712.02506 · Physical Review A

Bound state and localization of excitation in many-body open systems

H. T. Cui, H. Z. Shen, S. C. Hou, X. X. Yi

Published Apr 30, 2018• 8 citations
arXivHTMLPDF

Abstract

We study the exact bound state and time evolution for single excitations in one-dimensional $XXZ$ spin chains within a non-Markovian reservoir. For the bound state, a common feature is the localization of single excitations, which means the spontaneous emission of excitations into the reservoir is prohibited. Exceptionally, the pseudo-bound state can be found, for which the single excitation has a finite probability of emission into the reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists, and it is also the pseudo-bound state. The effect of quasirandom disorder in the spin chain is also discussed; such disorder induces the single excitation to locate at some spin sites. Furthermore, to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitations in spin chains is studied exactly. An interesting observation is that the excitation can stay at its initial location with high probability only when the bound state and disorder coexist. In contrast, when either one of them is absent, the information of the initial state can be erased completely or becomes mixed. This finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.

DOI
10.1103/physreva.97.042129

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We study the exact bound state and time evolution for single excitations in one-dimensional XXZXXZXXZ spin chains within a non-Markovian reservoir. For the bound state, a common feature is the localization of single excitations, which means the spontaneous emission of excitations into the reservoir is prohibited. Exceptionally, the pseudo-bound state can be found, for which the single excitation has a finite probability of emission into the reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists, and it is also the pseudo-bound state. The effect of quasirandom disorder in the spin chain is also discussed; such disorder induces the single excitation to locate at some spin sites. Furthermore, to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitations in spin chains is studied exactly. An interesting observation is that the excitation can stay at its initial location with high probability only when the bound state and disorder coexist. In contrast, when either one of them is absent, the information of the initial state can be erased completely or becomes mixed. This finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.
Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently however, it has been established that disorder can localize an isolated many body system, potentially allowing for a sharply defined topological phase even in a highly excited state. Here we show this to be the case for the topological phase of a one dimensional magnet with quenched disorder, which features spin one-half excitations at the edges. The time evolution of a simple, highly excited, initial state is used to reveal quantum coherent edge spins. In particular, we demonstrate, using theoretical arguments and numerical simulation, the coherent revival of an edge spin over a time scale that grows exponentially bigger with system size. This is in sharp contrast to the general expectation that quantum bits strongly coupled to a 'hot' many body system will rapidly lose coherence.
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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 examine different nonlinear open quantum systems and calculate the non-Markovianity based on the distinguishability between two density matrices. We show that for a single spin (qubit) coupled to a bosonic field the non-Markovianity depends on the spectral density function and can take on any number N with 0 ≤ N ≤ 1, meaning the dynamics can be Markovian or highly non-Markovian. For the main result we consider a system of Ntot identical spins coupled to an environment in the mean-field way. Each spin is coupled to a local and the common reservoir. There are only indirect interactions between the spins through the common reservoir. In limit Ntot → 1 the subsystem consisting of a fixed set of n particles reduces to a factorized state in which each factor is a single spin evolving according to a nonlinear Hartree-Lindblad equation which is exactly solvable. For non-stationary initial spin states the non-Markovianity diverges. In this instance we can never approximate the dynamics of the quantum system by a Markovian master equation and this implies that in the mean field models, memory effects are significant.
We investigate the effect of a non-Markovian, structured reservoir on an open Heisenberg spin chain. We establish a coherent self-feedback mechanism as the reservoir couples frequency dependently to the spin chain. Thus, loss and driving take place due to the interaction of the spin chain with its own past. This new paradigm of non-Markovian imposed boundary driving allows discussion of a new kind of nonequilibrium steady state. We show that for certain parameters, even in the long-time limit, persistent oscillations occur within the chain. Moreover, we demonstrate that the conditions for these oscillations and excitation trapping depend on the characteristics of the chain, thus making it possible to characterize a chain by detection of its emitted signal under influence of self-feedback.
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.