Wimberger, Sandro and Schlagheck, Peter and Mannella, Riccardo
Tunnelling rates for the nonlinear Wannier-Stark problem.
Journal of Physics B 39, p. 729.
Other URL: http://www.iop.org/EJ/S/3/255/abstract/0953-4075/39/3/024
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.