Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Stable islands in chaotic atom-optics billiards, caused by curved trajectories

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

Published Apr 24, 2002• 32 citations
Publisher

Abstract

We investigate the effects of curving trajectories by applying external force fields on a particle in a billiard. We investigate two special cases: a constant force field and a parabolic potential. These perturbations change the stability conditions and can lead to formation of elliptical orbits in otherwise hyperbolic billiards. We demonstrate these effects experimentally with ultra-cold atoms in atom-optic billiards.

DOI
10.1088/0953-4075/35/9/315

Related papers

Controlling dynamics in atom-optics billiards with external force fields

Mikkel F. Andersen, Ariel Kaplan, N. Friedman +1 more

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.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

Observation of Islands of Stability in Soft Wall Atom-Optics Billiards

Ariel Kaplan, Nir Friedman, Mikkel F. Andersen +1 more

We report on numerical and experimental observations of islands of stability induced in a Bunimovich stadium atom-optics billiard by a soft wall repulsive potential. A deviation from exponential decay of the survival probability of atoms in an open billiard is observed, and explained by the presence of these stable islands and a sticky region surrounding them. We also investigate islands in dispersing billiards with soft walls, and predict a new mechanism for their formation.

Physical Review Letters•Dec 11, 2001•83 citations

Controlling the stability of motion in atom-optics billiards

N. Friedman, Ariel Kaplan, Dina Carasso +1 more

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.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•1 citation

Chaotic dynamics of ultra-cold atoms in optical billiards

Valery Milner, J. L. Hanssen, Wesley C. Campbell +1 more

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.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•2 citations

Observation of Chaotic and Regular Dynamics in Atom-Optics Billiards

Nir Friedman, Ariel Kaplan, Dina Carasso +1 more

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.

Physical Review Letters•Feb 19, 2001•209 citations

Dark optical traps for ultra-cold atoms

Nir Davidson

Dark optical traps use repulsive light forces to confine atoms mostly in the dark where their interaction with the trapping light is largely reduced, to enable long coherence times of the trapped atoms combined with tight confinement. We report on single-beam dark optical traps for ultra-cold atoms. These traps were used to demonstrate new spectroscopic and dynamical effects of the trapped atoms, including the observation of regular and chaotic motion in so called optical "billiards."

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 18, 2003•3 citations
We investigate the effects of curving trajectories by applying external force fields on a particle in a billiard. We investigate two special cases: a constant force field and a parabolic potential. These perturbations change the stability conditions and can lead to formation of elliptical orbits in otherwise hyperbolic billiards. We demonstrate these effects experimentally with ultra-cold atoms in atom-optic billiards.
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.
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.
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.
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.