Non-Markovian Quantum Exceptional Points

TL;DR

This paper develops a theoretical framework to analyze exceptional points in non-Markovian quantum systems, revealing new phenomena and potential for enhanced sensitivity through environmental engineering.

Contribution

It introduces a novel approach for identifying and studying non-Markovian exceptional points using exact numerical methods, expanding understanding beyond the Markovian regime.

Findings

Discovery of pure non-Markovian EPs unobservable in Markovian systems

EPs coincide with the transition from Markovian to non-Markovian dynamics

Structured environments can increase EP order and system sensitivity

Abstract

Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators, where eigenvalues and eigenvectors coalesce. Recently, open quantum systems have been increasingly explored as EP testbeds due to their natural non-Hermitian nature. However, existing works mostly focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. In this work, we address this gap by proposing a theoretical framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode mapping and the hierarchical equations of motion. The proposed framework enables conventional spectral analysis for EP identification, establishing direct links between EPs and dynamic manifestations in open systems, such as non-exponential decays and enhanced sensitivity to external perturbations. We unveil pure non-Markovian EPs that are unobservable in the Markovian limit. Remarkably, the EP aligns with the Markovian-to-non-Markovian transition, and the EP condition is adjustable by modifying environmental spectral properties. Moreover, we show that structured environments can elevate EP order, thereby enhancing the system's sensitivity. These findings lay a theoretical foundation and open new avenues for non-Markovian reservoir engineering and non-Hermitian physics.