  In this thesis, we investigate the quantum mechanical interaction of light
with matter in the form of a gas of ultracold atoms: the atomic ensemble. We
present a theoretical analysis of two problems, which involve the interaction
of quantized electromagnetic fields (called signal and idler) with the atomic
ensemble (i) cascade two-photon emission in an atomic ladder configuration, and
(ii) photon frequency conversion in an atomic diamond configuration. The
motivation of these studies comes from potential applications in long-distance
quantum communication where it is desirable to generate quantum correlations
between telecommunication wavelength light fields and ground level atomic
coherences. We develop a theory of correlated signal-idler pair correlation.
The analysis is complicated by the possible generation of multiple excitations
in the atomic ensemble. An analytical treatment is given in the limit of a
single excitation assuming adiabatic laser excitations. The analysis predicts
superradiant timescales in the idler emission in agreement with experimental
observation. To relax the restriction of a single excitation, we develop a
different theory of cascade emission, which is solved by numerical simulation
of classical stochastic differential equation using the theory of open quantum
systems. The simulations are in good qualitative agreement with the analytical
theory of superradiant timescales. We provide a quantum theory of near-infrared
to telecom wavelength conversion in the diamond configuration. The system
provides a crucial part of a quantum-repeater memory element, which enables a
"stored" near-infrared photon to be converted to a telecom wavelength for
transmission without the destruction of light-atom quantum correlation.
