Encircling the Liouvillian exceptional points: a brief review

TL;DR

This review discusses the significance of Liouvillian exceptional points in open quantum systems, highlighting their theoretical understanding, experimental observations, and potential for quantum applications, especially focusing on chiral state transfer phenomena.

Contribution

It provides a comprehensive overview of the dynamic effects of Liouvillian exceptional points, including recent experimental findings and insights into many-body collective phenomena.

Findings

Observation of chiral state transfer near Liouvillian exceptional points

Experimental realization in atomic systems such as ultracold atoms and superconducting qubits

Discussion of many-body effects and their implications for quantum technologies

Abstract

Exceptional points are the branch-point singularities of non-Hermitian Hamiltonians, and have rich consequences in open-system dynamics. While the exceptional points and their critical phenomena are widely studied in the non-Hermitian settings without quantum jumps, they also emerge in open quantum systems depicted by the Lindblad master equations, wherein they are identified as the degeneracies in the Liouvillian eigenspectrum. These Liouvillian exceptional points often have distinct properties compared to their counterparts in non-Hermitian Hamiltonians, leading to fundamental modifications of the steady states or the steady-state-approaching dynamics. Since the Liouvillian exceptional points widely exist in quantum systems such as the atomic vapours, superconducting qubits, and ultracold ions and atoms, they have received increasing amount of attention of late. Here we present a brief review on an important aspect of the dynamic consequence of Liouvillian exceptional points, namely the chiral state transfer induced by the parametric encircling the Liouvillian exceptional points. Our review focuses on the theoretical description and experimental observation of the phenomena in atomic systems that are experimentally accessible. We also discuss the on-going effort to unveil the collective dynamic phenomena close to the Liouvillian exceptional points, as a consequence of the many-body effects therein. Formally, these phenomena are the quantum-many-body counterparts to those in classical open systems with nonlinearity, but hold intriguing new potentials for quantum applications.