Atomic motion in magneto-optical double-well potentials: A testing ground for quantum chaos - art. no. 056119

We have identified ultracold atoms in magneto-optical double-well potential s as a very clean setting in which to study the quantum and classical dynam ics of a nonlinear system with multiple degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise f rom nonseparable couplings between the atomic spin and its center of mass m otion. The main features of the chaotic dynamics are analyzed using action- angle variables and Poincare surfaces of section. We show that for the init ial state prepared in current experiments [D. J. Haycock et al., Phys. Rev. Lett. 85, 3365 (2000)], classical and quantum expectation values diverge a fter a finite time, and the observed experimental dynamics is consistent wi th quantum-mechanical predictions. Furthermore, the motion corresponds to t unneling through a dynamical potential barrier. The coupling between the sp in and the motional subsystems, which are very different in nature from one another, leads to interesting questions regarding the transition from regu lar quantum dynamics to chaotic classical motion.