Survival, decay, and topological protection in non-Hermitian quantum transport

TL;DR

This paper develops a classification of topological phases in non-Hermitian quantum systems with decay, revealing how dark states and winding numbers govern protected transport and observable quantization.

Contribution

It introduces a framework using Bloch theory to classify topological dynamical phases in 1D non-Hermitian systems with absorbing sites, linking winding numbers to quantized observables.

Findings

Dark states are decoupled and immune to dissipation.

Quantized average particle displacement linked to winding numbers.

Topological transitions cause non-analytic changes in observables.

Abstract

Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which are decoupled from the environment and thus immune to dissipation. Here we develop a classification of topological dynamical phases for one-dimensional quantum systems with periodically-arranged absorbing sites. This is done using the framework of Bloch theory to describe the dark states and associated topological invariants. The observables, such as the average particle displacement over its life span, feature quantized contributions that are governed by the winding numbers of cycles around dark-state submanifolds in the Hamiltonian parameter space. Changes in the winding numbers at topological transitions are manifested in non-analytic behavior of the observables. We discuss the conditions under which nontrivial topological phases may be found, and provide examples that demonstrate how additional constraints or symmetries can lead to rich topological phase diagrams.