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American Journal of Physics

A quantum bouncing ball

Julio R. Gea-Banacloche

Published Sep 1, 1999• 125 citations
Publisher

Abstract

The dynamics of a quantum wave packet bouncing on a hard surface under the influence of gravity are studied. This is a system that might be realized experimentally with cold atoms dropped onto an “atomic mirror.” The classical limit is discussed and interesting departures from classical behavior are pointed out and explained.
DOI
10.1119/1.19124

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An optical realization of a quantum bouncing ball on a truncated lattice is theoretically proposed for light waves propagating near the edge of a circularly curved waveguide array. As compared to the analogous problem of matter waves bouncing on a perfectly reflecting surface under the influence of gravity, where the wave packets basically behave as classical particles, it is shown that the genuine quantum regimes of wave packet collapse and revival are accessible for the discrete optical system.
Almost everyone has spent hours as a child bouncing rubber balls on hard surfaces. Later, we learn that the ball is made up of tightly bound atoms. The same game has been played by physicists at the Ecole Normale Superieure (ENS) in Paris who have bounced a ball of trapped, cold caesium atoms more than eight times on a curved mirror created with laser light (C G Aminoff et al. Phys. Rev. Lett. (1993) 71 3083). This work could lead to experiments in which quantum collective effects of atoms play a major role.
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.
Abstract We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables.