Balancing gain and loss in symmetrised multi-well potentials

TL;DR

This paper explores how symmetrising multi-well quantum potentials with gain and loss can lead to stationary states, extending beyond PT-symmetry, with analytical solutions for two- and three-mode systems.

Contribution

It introduces a symmetrisation approach for multi-well potentials with gain and loss, providing analytical solutions and insights into stability and stationary states.

Findings

Symmetrisation enables real spectra in asymmetric open systems.

Only PT-symmetric two-mode systems can have stationary excited states.

Analytical solutions for two- and three-mode systems are derived.

Abstract

Balanced gain and loss leads to stationary dynamics in open systems. This occurs naturally in PT-symmetric systems, where the imaginary part of the potential describing gain and loss is perfectly antisymmetric. While this case seems intuitive, stationary dynamics are also possible in asymmetric open systems. Open multi-well quantum systems can possess completely or partly real spectra if their Hamiltonian is symmetrised or semi-symmetrised, respectively. In contrast to similar concepts, symmetrisation allows for the description of physical multi-well potentials with gain and loss. A simple matrix model for the description of two and three-mode systems is used as an example, for which analytical symmetrised solutions are derived. It is explicitly shown how symmetrisation can be used to systematically find two-mode systems with a stable, stationary ground state and why only PT-symmetric two-mode systems can have stationary excited states.