Topological dynamics and correspondences in composite exceptional rings

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. Exceptional points are non-Hermitian singularities where both eigenvalues and their corresponding eigenstates coalesce, presenting interesting spectral topology that has been observed in diverse platforms. The authors explore a special type of exceptional points structure, the composite exceptional ring, which combines third-order and Weyl exceptional rings to uncover new topological behaviors and they show their potential to predict and control mode transfer in non-Hermitian systems, with applications in quantum computing and metrology.