Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{PT}$-symmetric non-Hermitian systems

TL;DR

This paper investigates non-adiabatic transitions in non-Hermitian $ ext{PT}$-symmetric systems with exceptional points, deriving analytical formulas and discussing experimental realizations in optical waveguides.

Contribution

It provides new analytical approximations for non-adiabatic transition probabilities in $ ext{PT}$-symmetric systems with time-dependent exceptional points.

Findings

Different transmission dynamics identified across exceptional points

Analytical formulas for non-adiabatic transition probabilities derived

Potential experimental setups discussed with optical waveguides

Abstract

Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formulas for the non-adiabatic transmission probabilities. We discuss possible experimental realizations with a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian one-dimensional tight-binding optical waveguide lattice.