Exceptional Points in a $\mathcal{PT}$-symmetrical quantum system: a Scattering matrix approach

J. Colín-Gálvez, E. Castaño, G. Báez, V. Domínguez-Rocha

Published 2023-12-05Version 1

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