  In this dissertation, I explore interactions between matter and propagating
light. The electromagnetic field is modeled as a reservoir of quantum harmonic
oscillators successively streaming past a quantum system. Each weak and
fleeting interaction entangles the light and the system, and the light
continues its course. Within the framework of open quantum systems, the light
is eventually traced out, leaving the reduced quantum state of the system as
the primary mathematical subject. Two major results are presented. The first is
a master equation approach for a quantum system interacting with a traveling
wave packet prepared with a definite number of photons. In contrast to
quasi-classical states, such as coherent or thermal fields, these N-photon
states possess temporal mode entanglement, and local interactions in time have
nonlocal consequences. The second is a model for a three-dimensional
light-matter interface for an atomic ensemble interacting with a paraxial laser
beam and its application to the generation of QND spin squeezing. Both coherent
and incoherent dynamics due to spatially inhomogeneous atom-light coupling
across the ensemble are accounted for. Measurement of paraxially scattered
light can generate squeezing of an atomic spin wave, while diffusely scattered
photons lead to spatially local decoherence.
