Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential

TL;DR

This paper explores the dynamic behavior of exceptional points in non-Hermitian continuous quantum systems with imaginary potentials, revealing unique EP phenomena that could influence future quantum simulations.

Contribution

It introduces a continuous model with imaginary potentials to study EP dynamics, extending the understanding beyond discrete systems and highlighting new behaviors.

Findings

EPs exhibit dynamic manifestation in continuous systems

Distinct EP behaviors across different orders are demonstrated

Modeling via a non-Hermitian Stark ladder system is effective

Abstract

Exceptional points (EPs) are distinct characteristics of non-Hermitian Hamiltonians that have no counterparts in Hermitian systems. In this study, we focus on EPs in continuous systems rather than discrete non-Hermitian systems, which are commonly investigated in both the experimental and theoretical studies. The non-Hermiticity of the system stems from the local imaginary potential, which can be effectively achieved through particle loss in recent quantum simulation setups. Leveraging the discrete Fourier transform, the dynamics of EPs within the low-energy sector can be well modeled by a Stark ladder system under the influence of a non-Hermitian tilted potential. To illustrate this, we systematically investigate continuous systems with finite imaginary potential wells and demonstrate the distinctive EP dynamics across different orders. Our investigation sheds light on EP behaviors, potentially catalyzing further exploration of EP phenomena across a variety of quantum simulation setups.