Dynamical topology of chiral and nonreciprocal state transfers in a non-Hermitian quantum system

TL;DR

This paper explores the topological dynamics in non-Hermitian quantum systems, demonstrating robustness of chiral and nonreciprocal state transfers through experimental validation of dynamical invariants in a trapped ion setup.

Contribution

It introduces the concept of dynamical vorticity as a topological invariant and experimentally validates topological robustness in non-Hermitian quantum dynamics.

Findings

Topological dynamics are robust against perturbations.

Dynamical vorticity protects the topological features.

Quantum state tomography reveals symmetry breaking.

Abstract

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological phenomenon, known as topological dynamics, where the evolution process allows a hidden topological invariant associated with continuous flows. To validate this conjecture, we study topological chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. These dynamics are topologically robust against external perturbations even in the presence dissipation-induced nonadiabatic processes. Our findings indicate that they are protected by dynamical vorticity -- an emerging topological invariant associated with the energy dispersion of non-Hermitian band structures in a parallel transported eigenbasis. The symmetry breaking and other key features of topological dynamics are directly observed through quantum state tomography. Our results mark a significant step towards exploring topological properties of open quantum systems.