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arXiv:cond-mat/0404608 · Physical Review A

Landau-Zener tunneling of Bose-Einstein condensates in an optical lattice

V. V. Konotop, P. G. Kevrekidis, Mario Salerno

Published Aug 18, 2005• 39 citations
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Abstract

A theory of the nonsymmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a set of linearly coupled nonlinear Schr\"odinger equations. The key role of the modulational instability in rendering the interband transitions irreversible is highlighted.

DOI
10.1103/physreva.72.023611

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A theory of the nonsymmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a set of linearly coupled nonlinear Schr"odinger equations. The key role of the modulational instability in rendering the interband transitions irreversible is highlighted.
In this paper, we develop a theory of the LZ tunneling between the lowest bands of a periodic potential. Our approach reveals the role of modulational instability (MI) on the atom transfer between zones as well as the effect of (partial) suppression of the MI by the lattice acceleration. Our consideration is based on the Gross-Pitaevskii equation, which in the two-zone approximation is reduced to the linearly coupled nonlinear Schrodinger equations. In the presence of nonlinearity, the Bloch states can become unstable and localized states can appear in the gaps between bands (gap-solitons) in which can dramatically affect the atomic transfer rate. The stability properties constitute the main reason of asymmetry of the LZ tunneling
In BECs, collisions between condensate atoms give rise to a nonlinear contribution to the dynamics which is typically included as a mean-field term in the Schrodinger equation. This nonlinearity leads to a modification of well-known effects associated with matter waves in periodic potentials and adds a number of phenomena that are absent in the linear problem. We focused on the dynamics of a BEC in an accelerated optical lattice. In the linear case, this gives rise to Bloch oscillations and, above a critical acceleration, to Landau-Zener tunneling. In the nonlinear case, the probability for Landau-Zener tunneling is modified depending on the direction in which it occurs between two bands. By varying the acceleration of the optical lattice and measuring the time-dependence of the interference contrast, we were able to identify the instability regime and the characteristic time in which the dynamical instability destroys the interference pattern. Furthermore, we observed an increase in the condensate dimensions perpendicular to the lattice direction when the unstable region was reached. This indicates a mechanism whereby the longitudinal instability leads to an increase in the transverse release energy
We present our experimental investigations on the subject of dynamical nonlinearity-induced instabilities and of nonlinear Landau-Zener tunneling between two energy bands in a Rubidium Bose-Einstein condensate in an accelerated periodic potential. These two effects may be considered two different regimes (for small and large acceleration) of the same physical system and studied with the same experimental protocol. Nonlinearity introduces an asymmetry in Landau-Zener tunneling; as a result, tunneling from the ground state to the excited state is enhanced whereas in the opposite direction it is suppressed. When the acceleration is lowered, the condensate exhibits an unstable behaviour due to nonlinearity. We also carried out a full numerical simulation of both regimes integrating the full Gross-Pitaevskii equation; for the Landau-Zener effect we also used a simple two-level model. In both cases we found good agreement with the experimental results.
From a two-level model for nonlinear Landau-Zener tunnelling between two energy bands of a Bose-Einstein condensate in a periodic potential we obtain unequal tunnelling rates for the two directions of tunnelling. With increasing nonlinearity, tunnelling from the ground state to the excited state is enhanced, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunnelling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry. We discuss the limitations of our approach and possible future experiments.