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arXiv:0712.3866 · New Journal of Physics

Resonant tunneling of Bose–Einstein condensates in optical lattices

Alessandro Zenesini, Carlo Sias, Hans Lignier, Yeshpal Singh, D. Ciampini, O. Morsch, R. Mannella, E. Arimondo, Andrea Tomadin, Sandro Wimberger

Published May 29, 2008• 47 citations
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Abstract

In this paper, we present the theoretical as well as experimental results on resonantly enhanced tunneling of Bose–Einstein condensates in optical lattices both in the linear case and for small nonlinearities. Our results demonstrate the usefulness of condensates in optical lattices for simulating Hamiltonians originally used for describing solid-state phenomena.

DOI
10.1088/1367-2630/10/5/053038

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In this paper, we present the theoretical as well as experimental results on resonantly enhanced tunneling of Bose–Einstein condensates in optical lattices both in the linear case and for small nonlinearities. Our results demonstrate the usefulness of condensates in optical lattices for simulating Hamiltonians originally used for describing solid-state phenomena.
We have observed tunneling suppression and photon-assisted tunneling of Bose-Einstein condensates in an optical lattice subjected to a constant force plus a sinusoidal shaking. For a sufficiently large constant force, the ground energy levels of the lattice are shifted out of resonance and tunneling is suppressed; when the shaking is switched on, the levels are coupled by low-frequency photons and tunneling resumes. Our results agree well with theoretical predictions and demonstrate the usefulness of optical lattices for studying solid-state phenomena.
Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
Quantum theory of the intraband resonant tunneling of a Bose-Einstein condensate loaded in a two-dimensional optical lattice is considered. It is shown that the phenomena of quantum collapse and revival can be observed in the fully quantum problem. The mean-field limit of the theory is analyzed using the WKB approximation for discrete equations, establishing in this way a direct connection between the two approaches conventionally used in very different physical contexts. More specifically we show that there exist two different regimes of tunneling and study dependence of quantum collapse and revival on the number of condensed atoms.