Nonlinear Coupled Quantum Dynamics of Photons and Atoms

We propose to investigate the quantum dynamics of model systems involving several atoms and/or photons with a strongly coupled time evolution. We will concentrate on three main examples namely (a) few atoms strongly coupled to a single cavity mode (cavity QED), (b) many dipole-dipole coupled atoms in a periodic external optical potential (optical lattices) and (c) many photons in several cavity modes coupled by a non-linear intracavity medium (quantum structures). (a) The first part deals With photons and atoms in small but high-Q optical cavities. Such systems are realized by putting high quality optical mirrors around a linear ion trap, a dark-spot magneto-optical trap (MOT), an atomic fountain or even a Bose condensate. A possible laser-like operation of these systems and the resulting radiation characteristics are discussed, as well as the possibility how to "lift" the microscopic quantum correlations of atoms to a "macroscopic" level maintaining coherence. We extend existing cavity QED models by including the external quantum motion of the atom(s). Under certain conditions the damped cavity field can lead to motional cooling and trapping of the atoms. (b) The second part treats the dynamics of atoms in optical lattices and superlattices. In particular we try to incorporate the effect of atomic dipole-dipole coupling and quantum statistics into the rate equations for the atomic populations and discuss substantial differences in the resulting effective non-linear dynamics between dark (blue detuned) and bright (red detuned) lattices. (c) In the third part we investigate the non-linear coupling of photons in a high Q cavity with an internal non-linear c (2) -medium. In a multimode situation as found in an OPO with quasi-planar or quasi-spherical resonator, spatial instabilities lead to a spontaneous formation of transverse optical patterns above threshold, which can be found again in the photon correlations below threshold. In addition we plan to generalize existing models to unstable cavity configurations and study the influence of excess quantum noise on the non-linear dynamics.