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Tunnelling rates for the nonlinear Wannier-Stark problem

Sandro Wimberger·Peter Schlagheck·Riccardo Mannella
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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.

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Sandro Wimberger, Peter Schlagheck, Riccardo Mannella. 2005-12-19. Tunnelling rates for the nonlinear Wannier-Stark problem. https://doi.org/10.1088/0953-4075%2F39%2F3%2F024

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