Topological Braiding and Dynamic Probing of Phase Transitions at Temporal Interfaces in Non-Hermitian Synthetic Dimensions

TL;DR

This paper explores topological phenomena at temporal interfaces in non-Hermitian systems, revealing a braiding structure in reflection and refraction coefficients and proposing a dynamical probe for phase transitions.

Contribution

It introduces the concept of topological braiding at temporal interfaces and links it to topological invariants, advancing understanding of non-Hermitian topological dynamics.

Findings

Reflection and refraction coefficients exhibit topological braiding structure.

Topological invariants determine the braiding pattern across the interface.

Proposed a dynamical probe to detect topological phase transitions.

Abstract

Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian in a one-dimensional non-Hermitian sys tem,the ensuring temporal interface excites both reflected and refracted wave modes. By intro ducing a chiral-symmetric Hamiltonian, this study reveals the topological effects at such temporal interfaces. We find that the reflection and refraction coefficients exhibit a topological braiding struc ture. This structure is directly determined by the difference in the topological invariants across the interface, establishing a bulk-boundary correspondence for temporal interfaces in non-Hermitian systems. Furthermore, we propose a dynamical probe that leverages the geometric similarity of eigenstates at the temporal interface to detect topological phase transitions. These findings estab lish a fundamental connection between topological braiding and nonreciprocal dynamics at temporal interfaces, providing a platform to explore phase transition detection and nonreciprocal phenomena in time-varying non-Hermitian systems.