Liouvillian topology and non-reciprocal dynamics in open Floquet chains

TL;DR

This paper introduces a microscopic model of open quantum systems with Floquet driving that reveals new topological phases and non-reciprocal transport phenomena, connecting non-Hermitian spectral properties with physical dynamics.

Contribution

It extends the analysis of non-Hermitian topological phases by including quantum jump processes, uncovering a jump-induced topological phase and demonstrating the NH skin effect in transient dynamics.

Findings

Discovery of a jump-induced topological phase.

Observation of NH skin effect in transient dynamics.

Link between NH spectral winding and non-reciprocal transport.

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 a 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 non-reciprocal 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.