Controlling atom -photon interactions in nano-structured media

Developing new techniques to control and manipulate the interaction between light and matter has been a central theme in science and engineering for many decades. These tools find wide-ranging applications in fields as diverse as spectroscopy, laser physics, and ultrafast science. Recently, there has been strong interest in extending this control down to the level of the constituent particles of light and matter, single atoms and single photons.;In this thesis, we explore several ways in which concepts from quantum optics and condensed matter physics can be combined with novel photonic systems to realize new tools for manipulating light-matter interactions. First, we theoretically and experimentally demonstrate that single quantum emitters can be strongly coupled to single surface plasmons (i.e., single photons) tightly guided on conducting nanowires. The strong coupling occurs due to the sub-diffraction-limit mode confinement, and can be used as a resource to efficiently collect emission or generate single photons. We also show theoretically that such a system can give rise to strong single-photon nonlinearities. As an application, we propose a scheme to realize a single-photon transistor, where the presence or absence of a single photon in a "gate" field regulates the propagation of a stream of "signal" photons.;We then describe how one-dimensional optical waveguides with tight field confinement can be used to create many-body photon gases with strong quantum mechanical correlations. In particular, we discuss a technique to dynamically create a "crystal" of photons starting from a non-interacting optical pulse. This "self-organization" process is mediated by effectively repulsive nonlinearities in the system.;Finally, we develop techniques to treat many-body, dipole-dipole interactions between atoms in an optical lattice. Using this formalism, we show that an optical band gap can form in a near-resonant lattice, which can be used to suppress the spontaneous emission of a single defect atom in the lattice, or couple a pair of distant defects through modified dipolar interactions. This formalism is also applied to calculate the frequency shifts in a lattice-based atomic clock due to dipolar interactions.