Signature of exceptional point phase transition in Hermitian systems

TL;DR

This paper reveals that signatures of exceptional point phase transitions, typically associated with non-Hermitian systems, can also be observed in Hermitian systems without dissipation, through specific coupled oscillators and their environment.

Contribution

It demonstrates the existence of EP phase transition signatures in Hermitian systems, expanding potential applications beyond non-Hermitian systems with dissipation.

Findings

Transition at coupling strength matches EP in non-Hermitian systems

Signature persists in non-Markovian dynamics with energy revivals

Proposes experimental scheme for observing the phenomenon

Abstract

Exceptional point (EP) is a spectral singularity in non-Hermitian systems. The passing over the EP leads to a phase transition, which endows the system with unconventional features that find a wide range of applications. However, the need of using the dissipation and amplification limits the possible applications of systems with the EP. In this work, we demonstrate an existence of signature of exceptional point phase transition in Hermitian systems that are free from dissipation and amplification. We consider a composite Hermitian system including both two coupled oscillators and their environment consisting only of several tens of degrees of freedom. We show that the dynamics of such a Hermitian system demonstrate a transition, which occurs at the coupling strength between oscillators corresponding to the EP in the non-Hermitian system. This transition manifests itself even in the non-Markovian regime of the system dynamics in which collapses and revivals of the energy occur. Thus, we demonstrate that the phase transition occurring at the passing over the EP in the non-Hermitian system manifests itself in the Hermitian system at all time. We discuss the experimental scheme to observe the signature of EP phase transition in the non-Markovian regime.