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The rise and fall of the amplitude, and phase, around Exceptional Points: a Scattering matrix approach

Abstract

We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with PT symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter γ. By varying γ the system resonances, which are naturally separated, coalesce at the exceptional point (EP). The transmission spectrum is obtained by means of the scattering matrix (S matrix) formalism and we examine the wave functions corresponding to the resonances as a function of γ. Specifically, we look for the behavior and distribution of the phases of the S matrix before, at and after the EP.

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