N-channel parity-time symmetry

TL;DR

This paper analyzes the eigenvalues of N-channel systems with parity-time symmetry, revealing phase mixing phenomena and conditions for symmetric and broken phases based on system parameters.

Contribution

It provides a general calculation of eigenvalues for N-channel parity-time symmetric systems and identifies conditions for phase mixing and symmetry breaking.

Findings

Eigenvalues show mixing of PT symmetric and broken phases.

At least four channels are needed for phase mixing without additional degrees of freedom.

Remaining eigenvalues are either PT symmetric or broken depending on parameters.

Abstract

We calculated the eigenvalues for a general N-channel coupled system with parity-time symmetry due to equal loss/gain. We found that the eigenspectrum displays a mixing of parity-time symmetric and broken phases, with N-2 of the eigenvalues being parity-time broken whereas the remaining two being either parity-time symmetric or broken depending on the loss/gain and coupling parameters. Our results also show that mixing of parity-time symmetric and parity-time broken phases can only be obtained for at least four-channels if other degrees of freedom like polarization is not taken into account.