Non-chiral non-Bloch invariants and topological phase diagram in non-unitary quantum dynamics without chiral symmetry

TL;DR

This paper introduces non-chiral non-Bloch invariants to characterize topological phases in non-Hermitian, non-unitary quantum systems without chiral symmetry, supported by experimental validation using photonic quantum walks.

Contribution

It defines and experimentally verifies non-chiral non-Bloch invariants for non-Hermitian systems lacking chiral symmetry, expanding topological classification methods.

Findings

Identification of non-Bloch topological phase diagram in 1D non-Hermitian systems

Experimental measurement of displacement moments correlates with topological invariants

Demonstration of topological phase distinctions without chiral symmetry

Abstract

The non-Bloch topology leads to the emergence of various counter-intuitive phenomena in non-Hermitian systems under the open boundary condition (OBC), which can not find a counterpart in Hermitian systems. However, in the non-Hermitian system without chiral symmetry, being ubiquitous in nature, exploring its non-Bloch topology has so far eluded experimental effort. Here by introducing the concept of non-chiral non-Bloch invariants, we theoretically predict and experimentally identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry in discrete-time non-unitary quantum walks of single photons. Interestingly, we find that such topological invariants not only can distinguish topologically distinct gapped phases, but also faithfully capture the corresponding gap closing in open-boundary spectrum at the phase boundary. Different topological regions are experimentally identified by measuring the featured discontinuities of the higher moments of the walker's displacement, which amazingly match excellently with our defined non-Bloch invariants. Our work provides a useful platform to study the interplay among topology, symmetries and the non-Hermiticity.