Tunnelling rates for the nonlinear Wannier-Stark problem

TL;DR

This paper introduces a numerical method to accurately compute tunnelling rates in a nonlinear Bose-Einstein condensate, revealing how weak nonlinearities significantly affect resonant tunnelling peaks.

Contribution

The authors develop a real-time integration technique for the complex-scaled Gross-Pitaevskii equation to find stationary eigenvalues in the nonlinear Wannier-Stark problem.

Findings

Weak nonlinearities significantly alter tunnelling peaks.

Mean-field interactions cause broadening and shifting of resonant peaks.

Analytic perturbation theory explains the peak shifts.

Abstract

We present a method to numerically compute accurate tunnelling rates for a Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii equation. Our method is based on a sophisticated real-time integration of the complex-scaled Gross-Pitaevskii equation, and it is capable of finding the stationary eigenvalues for the Wannier-Stark problem. We show that even weak nonlinearities have significant effects in the vicinity of very sensitive resonant tunnelling peaks, which occur in the rates as a function of the Stark field amplitude. The mean-field interaction induces a broadening and a shift of the peaks, and the latter is explained by analytic perturbation theory.