  The transport of ultra-cold atoms in magneto-optical potentials provides a
clean setting in which to investigate the distinct predictions of classical
versus quantum dynamics for a system with coupled degrees of freedom. In this
system, entanglement at the quantum level and chaos at the classical level
arise from the coupling between the atomic spin and its center-of- mass motion.
Experiments, performed deep in the quantum regime, correspond to dynamic
quantum tunneling. This nonclassical behavior is contrasted with the
predictions for an initial phase space distribution produced in the experiment,
but undergoing classical Hamiltonian flow. We study conditions under which the
trapped atoms can be made to exhibit classical dynamics through the process of
continuous measurement, which localizes the probability distribution to phase
space trajectories, consistent with the uncertainty principle and quantum
back-action noise. This method allows us to analytically and numerically
identify the quantum-classical boundary.
