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We compare the classical and quantum-mechanical motion of a distribution initially localized on a classical second-order resonance of a driven pendulum. As the driving is increased the quantum state becomes localized about the classically stable region of phase space. The existence of a parity symmetry then allows for coherent tunneling between isolated second-order resonances. We compare and contrast the classical and quantum behavior with the aid of perturbation theory. PACS number(s): 05.45.+b, 42.50.Vk

It is proposed that the atomic optical system of an ytterbium atom in a time-dependent optical standing wave be used to experimentally observe quantum nonlinear motion and, in particular, predict the quantum behavior of a system whose classical analog ranges from completely integrable, to near integrable, and finally to globally chaotic motion. We extend previous treatments to include spontaneous emission. From the study of theoretical models of dissipative quantum nonlinear motion, it is known that even small amounts of dissipation can significantly alter the quantum dynamics through the destruction of coherences. In this paper we present some theoretical and numerical results of the effect of spontaneous emission on nonlinear nonintegrable dynamics in atomic optics. When spontaneous emission is included, we show that the nature of the light-atom interaction introduces interesting features not usually investigated in models of dissipative quantum nonlinear dynamics. These include a potential that depends on the atom's internal state, a band structure, and a time-dependent dissipative process. PACS number(s): 42.50.Vk, 05.45.+b

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