Regular and chaotic quantum motions

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.

Jian‐Min Yuan, D.H. Feng, George M. Zaslavsky

Asher Peres

The evolution of a quantum state is altered when a small perturbation is added to the Hamiltonian. As time progresses, the overlap of the perturbed and unperturbed states gives an indication of the stability of quantum motion. It is shown that if a quantum system has a classically chaotic analog, this overlap tends to a very small value, with small fluctuations. On the other hand, if the classical analog is regular, the overlap remains appreciable (on a time average) and its fluctuations are much larger.

Boris V. Chirikov

I. Puha

Gerard J Milburn

A nonlinear, kicked quantum optical system, which classically exhibits regions of regular and chaotic motion, is proposed as a possible experimental test of quantum chaos. The mean photon number is shown to undergo regular collapse and revival in the regular region of phase space and irregular revivals in the chaotic region.