Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonia ns are time dependent. Thus we shall consider systems with a potential func tion that has a higher than quadratic dependence on the position and, furth ermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit cha otic dynamics. I shall show how such systems can be realized in atom optics , where very cord atoms interact with optical dipole potentials of a far-of f resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planc k's constant, (ii) the systems are almost perfectly isolated from the decoh ering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.