Non-Hermitian coherent states for finite-dimensional systems

TL;DR

This paper introduces non-Hermitian Gilmore-Perelomov coherent states for non-unitary representations, compares them with traditional states, and demonstrates their application in modeling light propagation in PT-symmetric optical systems.

Contribution

It extends coherent state theory to non-unitary representations and applies it to finite-dimensional $SU(1,1)$ systems in optics.

Findings

Non-Hermitian coherent states can be constructed for non-unitary group representations.

These states exhibit similarities and differences with traditional coherent states.

Application to PT-symmetric optical devices demonstrates practical relevance.

Abstract

We introduce Gilmore-Perelomov coherent states for non-unitary representations of non-compact groups, and discuss the main similarities and differences with respect to ordinary unitary Gilmore-Perelomov coherent states. The example of coherent states for the non-unitary finite dimensional representations of $SU(1,1)$ is considered and they are used to describe the propagation of light in coupled PT-symmetric optical devices.