Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system

TL;DR

This paper explores counter-intuitive scattering behaviors in PT-symmetric non-Hermitian systems, revealing divergent transmission peaks at weak non-Hermiticity and conventional Fabry-Perot resonances at strong non-Hermiticity, with unitarity recovery at extreme non-Hermiticity.

Contribution

It uncovers novel resonance phenomena in PT-symmetric systems, contrasting typical non-Hermitian behaviors and analyzing unitarity across different non-Hermiticity regimes.

Findings

Divergent transmission peaks occur at weak non-Hermiticity.

Conventional Fabry-Perot resonances reappear at strong non-Hermiticity.

Unitarity is broken in both regimes but restored at infinite non-Hermiticity.

Abstract

In non-Hermitian scattering problems the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and from the scattering system. In the present paper, we consider the scattering problem of a PT-symmetric potential and find a counter-intuitive behavior. In the usual PT-symmetric non-Hermitian system, we would typically find stationary semi-Hermitian dynamics in a regime of weak non-Hermiticity but observe instability once the non-Hermiticity goes beyond an exceptional point. Here, in contrast, the behavior of the transmission probability is strongly non-Hermitian in the regime of weak non-Hermiticity with divergent peaks, while it is superficially Hermitian in the regime of strong non-Hermiticity, recovering the conventional Fabry-Perot-type peak structure. We show that the unitarity of the S-matrix is generally broken in both of the regimes, but is recovered in the limit of infinitely strong non-Hermiticity.