Quantum and Classical Dynamics of Atoms in a Magneto-Optical Lattice

We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise from nonseparable couplings between the atomic spin and its center of mass motion. We have analyzed the distinct predictions of classical and quantum theory in this system in order to study quantum-classical correspondence and the quantum to classical transition. The classical version of the Hamiltonian corresponds to a magnetic moment moving in a spatially inhomogeneous magnetic field. The main features of the chaotic dynamics are analyzed using action-angle variables and Poincaré surfaces of section. We present a physical picture of the primary resonances and quantify the chaos by