Dynamics of photon-photon scattering in rubidium vapor

Experimental and theoretical approaches are used to investigate the domain of validity of an analogy between the nonlinear Fabry-Perot interferometer (NLFP) and the one- or two-dimensional weakly-interacting Bose gas. The former is an experimentally accessible nonlinear optical system, the latter is an interesting model system in condensed matter physics. The analogy is shown to hold in the mean-field description, and the challenges for a microscopic analogy are presented.; Traditional macroscopic and microscopic methods of theoretical quantum optics are reviewed. Phenomenological quantization procedures are difficult to apply to the NLFP, which requires resonant optical nonlinearities to generate interesting interparticle correlations. Scully-Lamb and phase-space microscopic theories have difficulty with the continuum of transverse modes in the NLFP geometry. Both approaches proceed in most cases by elimination of atomic degrees of freedom to produce an effective theory.; A simple many-body microscopic theory is developed to treat the interactions among photons in a resonant, lossy medium and a geometry with a continuum of modes. Rubidium vapor is considered as a representative medium. The theory describes dressed photons interacting by atom-mediated momentum exchange.; The many-body theory is applied to a particular experimental configuration, right angle scattering in a rubidium vapor cell. This allows a test of the theory and provides a direct measurement of the time during which the medium is involved in the photon-photon interaction.; An experiment to observe atom-mediated photon-photon scattering is presented. A standing-wave geometry appropriate for phase-conjugation by degenerate four-wave mixing is used. Temporal and angular correlations of the scattering products are measured by single-photon detection and standard time-correlation techniques. The timescale is found to be determined by the momentum distribution of the atoms and thus faster than the timescale assumed by adiabatic elimination. Good agreement is found between theory and experiment.