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arXiv:1005.1138 · New Journal of Physics

Manipulation of coherent atom waves using accelerated two-dimensional optical lattices

Wei-Chih Ting, Dian-Jiun Han, Shin-Tza Wu

Published Aug 27, 2010• 0 citations
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Abstract

We study the dynamics of Bose–Einstein condensates in accelerated two-dimensional (2D) optical square lattices by numerically solving the Gross–Pitaevskii equation. We consider the regime with negligible mean-field interactions and examine in detail the pulses of atom clouds ejected from the condensate due to Landau–Zener tunnelling. The pulses exhibit patterned structures that can be understood from the momentum–space dynamics of the condensate. Apart from conceiving the realization of a pulsed 2D atom laser, we demonstrate that, by exploring the band structure of the lattice, the Landau–Zener tunnelling and Bragg reflection of the condensate inside the optical lattice can provide a means of manipulation of coherent atom waves.

DOI
10.1088/1367-2630/12/8/083059

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We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well-depth, Bloch oscillations were observed. Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied. In order to allow in-trap measurements of these phenomena, we dynamically compensated for the intrinsic micromotion of the atoms in our time-orbiting potential trap.
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.
Experiments on atomic Bose-Einstein condensates inside quasi-one-dimensional optical lattices and related developments in the realization of atom lasers are currently at the frontiers in atomic physics. We give a short review of theoretical progress in evaluating the coherent transport of matter in such configurations, which has been based on an adaptation of the Wannier function representation of quasi-particle states in periodic potentials and on the use of advanced numerical methods for the solution of the time-dependent Gross-Pitaevskii equation. We present various methods by which the band structure of the elementary excitations of a periodic condensate may be probed and describe in terms of Bloch oscillations the coherent emission of matter pulses from a condensate inside an optical lattice under the force of gravity. A harmonic force can be applied to a condensate inside a magnetic trap by a rapid displacement of the center of the trap and a transition of the condensate from superfluid to dissipative behavior is driven by superposing an optical lattice. Finally, in the superfluid regime the combination of a constant force and a harmonic force in the presence of an optical lattice drives Josephson-type oscillations of the condensate, leading to observable resonances and multimode behavior.
We report experimental results on the properties of Bose-Einstein condensates in one-dimensional optical lattices. By accelerating the lattice, we observed Bloch oscillations of the condensate in the lowest band, as well as Landau-Zener (LZ) tunneling into higher bands when the lattice depth was reduced and/or the acceleration of the lattice was increased. The dependence of the LZ tunneling rate on the condensate density was then related to mean-field effects modifying the effective potential acting on the condensate, yielding good agreement with recent theoretical work. We also present several methods for measuring the lattice depth and discuss the effects of the micromotion in the time-orbiting-potential trap on our experimental results.
We present a thorough analysis of the nonlinear tunneling of Bose-Einstein condensates in static and accelerating two-dimensional lattices within the framework of the mean-field approximation. We deal with nonseparable lattices, considering different initial atomic distributions in highly symmetric states. For an analytical description of the condensate before instabilities develop, we derive several few-mode models, analyzing essentially both nonlinear and quasilinear regimes of tunneling. By direct numerical simulations, we show that two-mode models provide an accurate description of tunneling when either initially two states are populated or tunneling occurs between two stable states. Otherwise, a two-mode model may give only useful qualitative hints for understanding tunneling, but does not reproduce many features of the phenomenon. This reflects the crucial role of instabilities developed due to two-body interactions resulting in a non-negligible population of the higher bands. This effect becomes even more pronounced in the case of accelerating lattices. In the latter case we show that the direction of the acceleration is a relevant physical parameter which affects the tunneling by changing the atomic rates at different symmetric states and by changing the numbers of bands involved in the atomic transfer.