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Journal of Physics B Atomic Molecular and Optical Physics

Periodic trajectories of cold atoms in a gravitational cavity

Ifan G. Hughes, Timothy Darlington, Edward A. Hinds

Published Jul 11, 2001• 14 citations
Publisher

Abstract

We study the classical dynamics of an atom bouncing on a concave reflector, which is sometimes called a gravitational cavity. Experiments and simulations have previously shown that atoms released from particular heights exhibit anomalously long storage times but no explanations for this have been offered hitherto. Here we show that the stability is associated with orbits where the atom moves on a cyclic trajectory. These have a lower loss rate from the cavity because they explore only a small part of the mirror surface compared with generic trajectories in neighbouring parts of phase space. We identify and classify them.

DOI
10.1088/0953-4075/34/14/308

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We study the classical dynamics of an atom bouncing on a concave reflector, which is sometimes called a gravitational cavity. Experiments and simulations have previously shown that atoms released from particular heights exhibit anomalously long storage times but no explanations for this have been offered hitherto. Here we show that the stability is associated with orbits where the atom moves on a cyclic trajectory. These have a lower loss rate from the cavity because they explore only a small part of the mirror surface compared with generic trajectories in neighbouring parts of phase space. We identify and classify them.
Abstract We consider classical dynamics of a one-dimensional system of N particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like an N-dimensional fictitious particle moving in an N-dimensional crystalline structure. Our classical analysis constitutes a basis for quantum research of novel time crystal phenomena in ultra-cold atoms bouncing on an oscillating atom mirror.
A curved mirror for atoms was made from an evanescent wave, formed by internal reflection of a quasiresonant laser beam at a curved glass surface. A cold cloud of cesium atoms was dropped onto the mirror and observed to rebound more than 8 times. The mirror size and reflectivity were studied, and reasonable agreement with a simple theory obtained. With 800 mW of laser power and a mirror of 1 mm diameter, we observed up to 73% of the atoms returning after each bounce, the losses being mostly during the free flight between bounces.
Multiple bounces of cold rubidium atoms have been observed for times up to one second in a trap formed by gravity and a 2 cm-diameter spherical mirror made from a sinusoidally magnetized floppy disk. We have studied the dynamics of the atoms bouncing in this trap from several different heights up to 40.5 mm and we conclude that the atoms are reflected specularly and with reflectivity 1.01(3). Slight roughness of the mirror is caused by harmonics in the magnetization of the surface and by discontinuities at the boundaries between recorded tracks. As the next step in this atom optics program we propose using a magnetic mirror to create a 2D atomic gas. We discuss how cold atoms can be loaded into the ground state of a static magnetic potential well that exists above the surface of the mirror as a consequence of the intermediate-field Zeeman effect.
We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer—a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of a falling particle. We find that some effects, such as the fact that a quantum particle hitting a moving mirror may bounce significantly higher than when the mirror is fixed, are in line with classical intuition. Other effects, such as the change in relative phases or in the current density in spatial regions arbitrarily far from the mirror are specifically quantum. We further discuss how the effects produced by a moving mirror could be observed in link with current experiments, in particular with cold neutrons.
We have designed a gravitational cavity for ultra-cold atoms using an atomic mirror made from an evanescent laser wave.By a temporal variation of the evanescent wave intensity, we have realized various atom optics components such as temporal slits and phase modulators.We have also designed an atom interferometer using this cavity which proves that the coherence of the de Broglie waves can be preserved during the bounce of the atoms on the mirror.Finally we show that an efficient cooling of the atoms inside the cavity can be achieved using a Sisyphus process during the bounce.
We consider, by analytical and numerical means, the dynamics of a matter-wave soliton bouncing on the reflecting surface (atomic mirror) under the influence of gravity, when twobody interactions between atoms are periodically modulated in time. The analytical description is based on the variational approach. The frequencies of small amplitude oscillations of the soliton's center-of-mass and width are obtained. Analytical predictions are compared to the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.