Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians

TL;DR

This paper solves for a time-dependent metric in a non-Hermitian Jaynes-Cummings model, revealing how broken $ ext{PT}$-symmetry causes unique entanglement dynamics with oscillations and decay.

Contribution

It provides the first explicit solution for the time-dependent metric operator in a non-Hermitian Jaynes-Cummings Hamiltonian and analyzes entanglement behavior across symmetry regimes.

Findings

Broken $ ext{PT}$-symmetry leads to decay in entanglement oscillations.

Unbroken symmetry exhibits stable oscillatory entanglement.

Significant difference in entanglement dynamics between regimes.

Abstract

We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a non-Hermitian interaction term leads to a spontaneously broken $\mathcal{PT}$-symmetric regime which manifests itself in the exotic time-evolution of entanglement. When the symmetry is broken, oscillatory modes transition into decay. As such that there is a drastic difference in behaviour between the broken and unbroken regimes.