Asymmetries in the tunneling probability of Bose-Einstein condensate in an accelerating optical lattice

TL;DR

This paper develops a two-band model for Bose-Einstein condensate tunneling in an accelerating optical lattice, revealing asymmetries in tunneling probabilities influenced by initial populations and phases, and compares it with the nonlinear Landau-Zener model.

Contribution

It introduces a novel two-band finite-dimensional model that accounts for Bloch band structure and initial conditions, explaining experimental observations and contrasting with existing models.

Findings

Tunneling probability depends strongly on initial populations and phases.

Asymmetry in sensitivity of tunneling to nonlinearity affects experimental outcomes.

The two-band model agrees with the nonlinear Landau-Zener model when only one band is initially populated.

Abstract

We derive a two-band finite-dimensional model for description of the condensate tunneling in an accelerating optical lattice, taking into account the fine Bloch band structure. The model reveals a very strong dependence of the final band populations on the initial populations and phases. Most importantly, additionally to the known asymmetric dependence on the nonlinearity, there is also a notable asymmetry in the sensitivity of the tunneling probability to the nonliearity-induced initial population of the Bloch band to which the tunneling takes place. This fact can explain the experimentally observed unexpected independence of the upper-to-lower tunneling probablity on the nonlinearity. Finally, we compare the predictions of the two-band model with that of the well-known nonlinear Landau-Zener model and find disagreement when the two bands are initially populated. The disagreement can be qualitative and reveals itself even for a negligible nonlinearity. However, the two models agree remarkably well if just one band is populated initially.