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Quantum Electronics and Laser Science Conference

Controlling dynamics in atom-optics billiards with external force fields

Mikkel F. Andersen, Ariel Kaplan, N. Friedman, Nir Davidson

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. We investigate classical dynamics of curved-trajectory billiards that would have been hyperbolic (i.e. billiards with non-vanishing Lyapunov exponent) if the particle had moved in straight lines. We introduce the curvature by applying external force fields on the particle. We analytically show that this can lead to the formation of elliptical orbits in hyperbolic billiards, and experimentally demonstrate these effects, using atom-optics billiards where ultracold atoms are trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics.

DOI
10.1109/qels.2002.1031104

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Summary form only given. The motion of a particle inside a closed area surrounded by reflecting walls can be integrable or chaotic, depending on the shape of the boundary. These billiards serve as a good and simple model to study chaotic dynamics both classically and quantum mechanically. Recently, we realized an "atom-optics billiard", where ultra-cold atoms are trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics. In this work we describe how scattering and wall softness influence the dynamics of the atoms, and destroy or create stability.
We report on experimental observations of chaotic and regular motion of ultracold atoms confined by a billiard-shaped optical dipole potential induced by a rapidly scanning laser beam. To investigate the dynamics of the atoms confined by such an "atom-optics" billiard we measure the decay of the number of trapped atoms through a hole on the boundary. A fast and purely exponential decay, the clear signature of chaotic motion, is found for a stadium billiard, but not for a circular or an elliptical billiard, in agreement with theory. We also investigated the effects of decoherence, velocity spread, and gravity on regular and chaotic motion.
Summary form only given. One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a dosed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off the beams of light. These beams create the desired spatial pattern, forming an "optical billiard". The system is extremely flexible due to the high level of control of the billiards geometry, the initial atomic sample, and the available measurement techniques. We find an excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new experimental testing ground for classical and quantum chaos.
One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a closed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off beams of light. These beams create the desired spatial pattern, forming an "optical billiard." We find excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new testing ground for classical and quantum chaos.