Exceptional Points in a non-Hermitian extension of the Jaynes-Cummings Hamiltonian

TL;DR

This paper explores the spectral properties of a non-Hermitian, PT-symmetric extension of the Jaynes-Cummings Hamiltonian, focusing on the occurrence and significance of exceptional points in a system with environment-induced decay.

Contribution

It introduces a non-Hermitian Jaynes-Cummings model with decay, analyzing the mathematical and physical implications of exceptional points in this context.

Findings

Identification of exceptional points in the spectrum

Clarification of their physical meaning

Insights into non-Hermitian quantum systems

Abstract

We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of {the} two-level system are allowed to decay because of the interaction with the environment, {and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energies for the fermion system. We focus our attention} on the occurrence of exceptional points in the spectrum of the Hamiltonian, clarifying its mathematical and physical meaning.