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Quantum Electronics and Laser Science Conference

Chaotic dynamics of ultra-cold atoms in optical billiards

Valery Milner, J. L. Hanssen, Wesley C. Campbell, Mark G. Raizen

Published Nov 13, 2002• 2 citations
Publisher

Abstract

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.

DOI
10.1109/qels.2001.961934

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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.
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. We consider the semiclassical orbits of cold atoms in an optical lattice with a magnetically-induced harmonic trap. When the laser beams are aligned with a principal axis of the trap, the atoms follow regular classical paths. But when the laser beams are tilted at an angle to the axis, the atoms undergo a controllable transition from regular motion to strong classical chaos. Our work introduces atom traps in a tilted laser field as a new type of quantum chaotic system that is accessible to experiment.