Non‐Adiabatic Transitions in Parabolic and Super‐Parabolic PT‐Symmetric Non‐Hermitian Systems in 1D Optical Waveguides

Abstract

Exceptional points, which are 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, non‐adiabatic transitions in non‐Hermitian PT‐symmetric systems are investigated, in which the exceptional points are driven through at finite speeds which are quadratic or cubic functions of time. Different transmission dynamics separated by exceptional points are identified, and analytical approximate formulas for the non‐adiabatic transmission probabilities are derived. Possible experimental realizations with a PT‐symmetric non‐Hermitian 1D tight‐binding optical waveguide lattice are discussed through non‐Hermitian Bloch oscillations between different bands.

Analytical Approximations for Generalized Landau-Zener Transitions in Multi-level Non-Hermitian Systems

“…Despite its evident importance, the non-Hermitian generalization of the two-level Landau-Zener transition has only recently been analyzed by Longstaff [25], the associated non-Hermitian Landau-Zener-Stuckelberg interferometry was analyzed by Shen [26], and the non-Hermitian generalization of the parabolic and super-parabolic models, in which the exceptional points are driven through at finite speeds which are quadratic or cubic functions of time has been analyzed by the authors [27]. Compared to the two-state scenario, the research of the non-Hermitian generalization of Landau-Zener non-adiabatic transitions in the multi-state scenario is still at its early stage.…”

“…Recently, the three-state non-Hermitian Landau-Zener model in the presence of an interaction with the outer environment has been considered [28], and the Landau-Zener transitions through a pair of higher order exceptional points has been analyzed by Melanathuru [29]. In this work, based on our analytical approximation methods used in previous researches [23,24,27], we will analyze the dynamics of a four-state non-Hermitian PT -symmetric system which directly passes through a collection of exceptional points.…”

Proximity‐Encirclement of Multiple Exceptional Points in Non‐Hermitian Photonic Waveguides

“…Such dynamics is stemmed from the irreversible nonadiabatic transitions (NATs) owing to the non-Hermiticity that spoils the adiabatic theorem. [21,31,32] Dynamical EP encirclement under adiabatic conditions was supposed to be sufficed albeit the NATs occur, as long as the system evolution is sufficient adiabatic. [22,24] The occurrence of NATs is pertinent to the Stokes phenomena of asymptotics where the nonadiabatic contributions are amplified, resulting in a predictable final state.…”