# Loschmidt echo and fidelity decay near an exceptional point

## TL;DR

This paper investigates the counterintuitive phenomenon where non-Hermitian systems near an exceptional point exhibit slower fidelity decay and better Loschmidt echo than Hermitian systems, despite significant spectral deformation.

## Contribution

It reveals a surprising deceleration of fidelity decay and improved Loschmidt echo in non-Hermitian systems near an EP, contrasting with expectations based on spectral changes.

## Key findings

- Fidelity decay slows down near an EP in certain non-Hermitian systems.
- Loschmidt echo is enhanced compared to Hermitian counterparts.
- Behavior demonstrated in a tight-binding lattice with an imaginary gauge field.

## Abstract

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.