Multi-barrier resonant tunneling for the one-dimensional nonlinear Schr\"odinger Equation

TL;DR

This paper investigates nonlinear resonant tunneling in a one-dimensional Schrödinger equation with multiple barriers, revealing complex transmission structures and symmetry-breaking phenomena, modeled effectively by a nonlinear oscillator approach.

Contribution

It introduces an analytical method to study nonlinear resonant transmission through multiple barriers and demonstrates the emergence of complex transmission features and symmetry breaking.

Findings

Observation of bistable transmission peaks.

Identification of looped structures in transmission coefficients.

Modeling results align with nonlinear oscillator predictions.

Abstract

For the stationary one-dimensional nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-) analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a single quantum well (respectively a double barrier) complicated (looped) structures are observed in the transmission coefficient which can be identified as the result of symmetry breaking similar to the emergence of self-trapping states in double well potentials. Furthermore it is shown that these results are well reproduced by a nonlinear oscillator model based on a small number of resonance eigenfunctions of the corresponding linear system.