Finite-dimensional model for the condensate tunnelling in an accelerating optical lattice

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2006-04, Vol.39 (8), p.1997-2011
• Main Authors: Shchesnovich, Valery S, Cavalcanti, Solange B
• Format: Article
• Language: English
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Matter waves; Physics
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/39/8/017

We derive a two-band finite-dimensional model for the description of the condensate tunnelling 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 tunnelling probability to the nonlinearity-induced initial population of the Bloch band to which the tunnelling takes place. This fact can explain the experimentally observed unexpected independence of the upper-to-lower tunnelling probability 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.