Detecting topological invariants in chiral symmetric insulators via losses

TL;DR

This paper demonstrates a method to detect topological invariants in chiral symmetric insulators using particle displacement observed through losses, applicable to various models including Floquet systems and disordered insulators.

Contribution

It introduces a measurement-based scheme to identify bulk winding numbers via losses, connecting non-Hermitian Hamiltonians with topological detection.

Findings

Detection of winding number via particle displacement with losses

Measurement efficiency affects detection time inversely

Applicable to static, Floquet, and disordered topological insulators

Abstract

We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Phys. Rev. Lett. 102, 065703 (2009). We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.