Liouvillian topology and nonreciprocal dynamics in open Floquet chains

Abstract

Open quantum systems far from thermal equilibrium can exhibit remarkable physical phenomena including topological properties without a direct equilibrium counterpart. Along these lines, in periodically driven-dissipative systems within the effective non-Hermitian (NH) Hamiltonian approximation spectral winding numbers have been linked to intriguing nonreciprocal transport properties. Here, going beyond an NH Hamiltonian description, we introduce and study a microscopic lattice model of a driven open quantum system described by a Markovian quantum master equation, which exhibits the mentioned spectral winding within an NH approximation. By encompassing quantum jump processes in the topological analysis, we uncover a distinct \emph{jump-induced} topological phase, which qualitatively corresponds to the richer nonreciprocal transport properties of the fully quantum model. In addition, we find that the NH skin effect, i.e., the accumulation of a macroscopic number of eigenstates at one end of the system, is already visible in the transient dynamics even for systems with periodic boundary conditions. Our results exemplify the subtle correspondence between NH topological properties and physical manifestations of Liouvillian topological properties in open quantum systems, thus providing a theoretical framework towards understanding unidirectional transport in quantum dissipative Floquet dynamics.

Updated to extended and published version. 16 pages, 10 figures

References in corpus (23)

• Topological Origin of Non-Hermitian Skin Effects
• Topological characterization of periodically-driven quantum systems
• Quantum trajectories and open many-body quantum systems
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Non-Hermitian topological phenomena: A review
• Topological Non-Hermitian skin effect
• Topological classification of dynamical phase transitions
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Floquet States in Open Quantum Systems
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Non-Hermitian Floquet Topological Matter -- A Review
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Helical Floquet Channels in 1D Lattices
• Symmetry and topological classification of Floquet non-Hermitian systems
• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Floquet Exceptional Topological Insulator
• Lindbladian versus Postselected Non-Hermitian Topology
• Engineering nonequilibrium steady states through Floquet Liouvillians
• Topology of Discrete Quantum Feedback Control
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• Limits of the non-Hermitian description of decay models