Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices

TL;DR

This paper investigates the nonlinear resonant tunneling behavior of Bose-Einstein condensates in tilted optical lattices, introducing a new computational method to analyze excited resonance states and their impact on tunneling decay rates.

Contribution

A novel grid relaxation method with complex absorbing potentials for calculating excited resonance states in the Gross-Pitaevskii equation.

Findings

Enhanced decay rates due to resonant coupling to excited states

Efficient computation across a wide parameter range

Detailed analysis of nonlinearity effects in tunneling

Abstract

We study the tunneling decay of a Bose-Einstein condensate out of tilted optical lattices within the mean-field approximation. We introduce a novel method to calculate also excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.