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

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.

15 pages, 8 figures (15 panels). Supplementary material is available at http://hatano-lab.iis.u-tokyo.ac.jp/hatano/FPR2020/

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Cited by in corpus (1)

• Transport characteristics of a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian system: Effect of environmental interaction