Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians

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 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.

Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems

“…However, in the time-dependent case the expectation values for the energy operator H(t) have been found to be real for some models in that regime and the two regimes are distinguished by qualitatively quite different types of behaviour. Besides the energy also other physical quantities display unusual physical behaviour, such as for instance the entropy [29,30,31]. So far all explicit solutions constructed thereafter have confirmed these charcteristics, but up to now a generic argument that explains the occurrence of them is still missing.…”