M. F. Andersen

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

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.

Atom-Optics Billiards

We developed a new experimental system (the “atom-optics billiard”) and demonstrated chaotic and regular dynamics of cold, optically trapped atoms. We show that the softness of the walls and additional optical potentials can be used to manipulate the structure of phase space.

Integrability, Chaos and Mixed Phase-Space in Atom Optics Billiards

The dynamics of particles inside billiards has been extensively investigated both classically and quantum mechanically, since this very simple system yet exhibits a rich variety of nonlinear dynamics phenomena [1]. Hence, billiards where used to explore the connections between classical and quantum chaos, and also to shed light on the origins of statistical mechanics. 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 [2]. In this work, we present numerical investigation and experimental realization of atom-optics billiards with ordered, chaotic or mixed phase-space dynamics.

Echo spectroscopy and atom optics billiards

Department of Physics of Complex Systems, Weizmann Institute of Science,Rehovot 76100, IsraelAbstractWe discuss a recently demonstrated type of microwave spectroscopy of trappedultra-cold atoms known as ”echo spectroscopy” [M.F. Andersen et. al., Phys. Rev.Lett., in press (2002)]. Echo spectroscopy can serve as an extremely sensitive ex-perimental tool for investigating quantum dynamics of trapped atoms even whena large number of states are thermally populated. We show numerical results forthe stability of eigenstates of an atom-optics billiard of the Bunimovich type, anddiscuss its behavior under different types of perturbations. Finally, we propose touse special geometrical constructions to make a dephasing free dipole trap.Key words:PACS: