Landau–Zener–Stückelberg interferometry in -symmetric optical waveguides

Abstract

We investigate theoretically the non-adiabatic transitions in a -symmetric lattice subject to a strong ac force. In an optical realization of the lattice, the curvature of the waveguides along the paraxial propagation direction plays the role of the external periodic force necessary to drive the system through an avoided level crossing. Analytical expressions for the transition probabilities after multiple passages are obtained within an effective two-mode approximation. We show that gain and losses of the light beam, as well as the relative occupation probabilities of the bands involved in the transitions, can be accurately managed upon tuning the parameters of the system and are particularly sensitive to the amplitude of the non-Hermitian component of the lattice. Numerical simulations for the complete system are found to agree very well with the approximate analytical results.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.