Topological Dynamics and Correspondences in Composite Exceptional Rings

TL;DR

This paper explores the topological properties of complex exceptional rings in non-Hermitian systems, linking Chern numbers to physical behaviors and proposing experimental realizations in cold atoms for advanced quantum applications.

Contribution

It establishes a direct correspondence between Chern numbers and behaviors of complex exceptional rings, expanding topological classification in non-Hermitian physics.

Findings

Band braiding correlates with nontrivial Chern numbers.

Chern numbers predict mode transfer during encircling.

Proposed cold atom schemes for realizing CER.

Abstract

The study of unconventional phases and elucidation of correspondences between topological invariants and their intriguing properties are pivotal in topological physics. Here, we investigate a complex exceptional ring (CER), composed of a third-order exceptional ring and multiple Weyl exceptional rings, and establish a direct correspondence between Chern numbers and the distinctive behaviors of these structures. We show that band braiding during quasistatic encircling processes correlates with nontrivial Chern numbers, resulting in triple (double) periodic spectra for topologically nontrivial (trivial) middle bands. Moreover, Chern numbers predict mode transfer during dynamical encircling. Experimental schemes for realizing CER in cold atoms are proposed, emphasizing the crucial role of Chern numbers as both measurable quantity and descriptor of exceptional physics in dissipative systems. This discovery broadens topological classifications in non-Hermitian systems, with promising applications in quantum computing and metrology.