Open quantum systems with loss and gain

TL;DR

This paper explores the properties of small open quantum systems described by non-Hermitian Hamiltonians, focusing on exceptional points where eigenvalues coalesce, revealing how gain and loss influence system behavior and eigenfunction phases.

Contribution

It analyzes the behavior of eigenvalues and eigenfunctions near exceptional points in open quantum systems with gain and loss, extending understanding beyond purely lossy systems.

Findings

Eigenvalues exhibit non-analytical behavior at exceptional points.

Eigenfunction phases are not rigid near EPs, allowing environmental information transfer.

Gain and loss layers influence system properties similarly to natural open quantum systems.

Abstract

We consider different properties of small open quantum systems coupled to an environment and described by a non-Hermitian Hamilton operator. Of special interest is the non-analytical behavior of the eigenvalues in the vicinity of singular points, the so-called exceptional points (EPs), at which the eigenvalues of two states coalesce and the corresponding eigenfunctions are linearly dependent from one another. The phases of the eigenfunctions are not rigid in approaching an EP and providing therewith the possibility to put information from the environment into the system. All characteristic properties of non-Hermitian quantum systems hold true not only for natural open quantum systems that suffer loss due to their embedding into the continuum of scattering wavefunctions. They appear also in systems coupled to different layers some of which provide gain to the system. Thereby gain and loss, respectively, may be fixed inside every layer, i.e. characteristic of it.