Parity-time symmetry with coherent atomic gases: a concise review on recent progress

Inspired by the discovery of real energy spectra of non-Hermitian Hamiltonians obeying parity-time ((Formula presented.)) symmetry, many proposals and relevant experiments have been suggested and implemented for the realization of (Formula presented.) -symmetric Hamiltonians in various physical systems. Among them (Formula presented.) -symmetric atomic gases are of great interest as they possess many unique advantages, including: (i) the possession of active (Formula presented.) symmetry with balanced optical gain and loss, (ii) the ability to be extended to high-dimensional ones, and (iii) the feasibility to acquire enhanced Kerr nonlinearity based on the resonance character between light and atoms. Here, we review the new progresses made on the study of (Formula presented.) symmetry in coherent atomic gases since our last review paper [Advances in Physics: X, 2, 737–783 (2017)]. Particularly, we focus on the newly emerged research topics in this direction, including nonlocal nonlinear effect, non-Hermitian quantum effect, exceptional point and associated phenomenon, and non-Hermitian skin effect with (Formula presented.) symmetry. Perspectives and potential applications of the subject are also discussed.