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arXiv:1612.01503 · Physical Review Letters

Localization in Open Quantum Systems

Igor Yusipov, Tetyana V. Laptyeva, S. Denisov, Mikhail Ivanchenko

Published Feb 16, 2017• 52 citations
arXivHTMLPDF

Abstract

In an isolated single-particle quantum system, a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that a proper dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting nontrivially on a pair of sites. Operators are parametrized by a uniform phase, which controls the selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in the asymptotic regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by intermode jumps.

DOI
10.1103/physrevlett.118.070402

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iScience•Dec 1, 2025•1 citation
In an isolated single-particle quantum system, a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that a proper dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting nontrivially on a pair of sites. Operators are parametrized by a uniform phase, which controls the selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in the asymptotic regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by intermode jumps.
In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence that is believed to restore normal diffusion. We demonstrate that for a class of experimentally feasible non-Hermitian dissipators, which admit signatures of localization in asymptotic states, quantum particle opts between diffusive and ballistic regimes, depending on the phase parameter of dissipators, with sticking about localization centers. In a diffusive regime, statistics of quantum jumps is non-Poissonian and has a power-law interval, a footprint of intermittent locking in Anderson modes. Ballistic propagation reflects dispersion of an ordered lattice and introduces the second timescale for jumps, resulting in non-nonmonotonous probability distribution. Hermitian dephasing dissipation makes localization features vanish, and Poissonian jump statistics along with normal diffusion are recovered.
The interplay between dissipation and localization in quantum systems has garnered significant attention due to its potential to manipulate transport properties and induce phase transitions. In this work, we explore the dissipation-induced extended-localized transition in a flat band model, where the system's asymptotic state can be controlled by tailored dissipative operators. By analyzing the steady-state density matrix and dissipative dynamics, we demonstrate that dissipation is able to drive the system to states dominated by either extended or localized modes, irrespective of the initial conditions. The control mechanism relies on the phase properties of the dissipative operators, which selectively favor specific eigenstates of the Hamiltonian. Our findings reveal that dissipation can be harnessed to induce transitions between extended and localized phases, offering a novel approach to manipulate quantum transport in flat band systems. This work not only deepens our understanding of dissipation-induced phenomena in flat band systems but also provides a new avenue for controlling quantum states in open systems.
Existence of Anderson localization is considered a manifestation of coherence of classical and quantum waves in disordered systems. Signatures of localization have been observed in condensed matter and cold atomic systems where the coupling to the environment can be significantly suppressed but not eliminated. In this work we explore the phenomena of localization in random Lindbladian dynamics describing open quantum systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. The jump operator mediating the interaction with the bath linked to each site has a power-law tail with an exponent ppp. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning ppp which remains stable in the presence of coherent hopping. Unlike the entanglement transition in the quantum trajectories of open systems, this transition is exhibited by the averaged steady state density matrix of the Lindbladian. The steady state in the localized phase is characterised by a heterogeneity in local population imbalance, while the jump operators exhibit a constant participation ratio of the sites they affect. Our work provides a novel realisation of localization physics in open quantum systems.
Dissipation is usually regarded as a source of decoherence that suppresses quantum interference and localization. Here we show that suitably engineered dissipation can instead be used to select localized or extended states in a strictly non-disordered one-dimensional lattice. The underlying clean lattice has spatially inhomogeneous hopping and supports both extended bulk states and localized boundary states, including an algebraically localized bound state in the continuum. We introduce a nonlocal bond jump operator with a tunable relative phase and show that this phase selectively favors eigenstates with different spatial phase correlations. As a result, the long-time density matrix can be steered toward sectors dominated by localized or extended Hamiltonian eigenstates without changing any Hamiltonian parameter. The microscopic origin of the selection is quantified by the fraction of site pairs separated by a distance lll that are phase matched with the dissipative channel. We further characterize the dissipative quench through the quantum fidelity and show that the selected character of the steady state can persist after the dissipation is removed. Our results establish phase-selective bond dissipation as a route to controllable state preparation and transport manipulation in non-disordered lattices.
Many-body localization (MBL) is a result of the balance between interference-based Anderson localization and many-body interactions in a high-dimensional Fock space. It is expected that dissipation is blurring interference and destroying that balance so that the asymptotic state of a system with an MBL Hamiltonian does not bear localization signatures. This is evidently true in the case of local dephasing which drives any system into an infinite-temperature state. We demonstrate, by using a set of dissipative operators, where each one is acting nontrivially on a pair of neighboring sites (or spins), that an MBL system can be brought into a Hamiltonian-specific steady state. The difference between ergodic and MBL Hamiltonians can be seen in statistics of imbalance, entanglement entropy, and level spacing of the steady-state density operator. By introducing pairwise dissipative operators into an MBL system already exposed to dephasing, these localization signatures can be restored.
The interplay between dissipation and localization in quantum systems has garnered significant attention due to its potential to manipulate transport properties and induce phase transitions. In this work, we explore the dissipation-induced extended-localized transition in a flat-band model, where the system's asymptotic state can be controlled by tailored dissipative operators. By analyzing the steady-state density matrix and dissipative dynamics, we demonstrate that dissipation is able to drive the system to states dominated by either extended or localized modes, irrespective of the initial conditions. The control mechanism relies on the phase properties of the dissipative operators, which selectively favor specific Hamiltonian eigenstates. Our findings reveal that dissipation can be harnessed to induce transitions between extended and localized phases, offering a novel approach to manipulate quantum transport in flat-band systems. This work not only deepens our understanding of dissipation-induced phenomena in flat-band systems but also provides a new avenue for controlling quantum states in open systems.