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In this thesis, we investigate the quantum mechanical interaction of lightwith matter in the form of a gas of ultracold atoms: the atomic ensemble. Wepresent a theoretical analysis of two problems, which involve the interactionof quantized electromagnetic fields (called signal and idler) with the atomicensemble (i) cascade two-photon emission in an atomic ladder configuration, and(ii) photon frequency conversion in an atomic diamond configuration. Themotivation of these studies comes from potential applications in long-distancequantum communication where it is desirable to generate quantum correlationsbetween telecommunication wavelength light fields and ground level atomiccoherences. We develop a theory of correlated signal-idler pair correlation.The analysis is complicated by the possible generation of multiple excitationsin the atomic ensemble. An analytical treatment is given in the limit of asingle excitation assuming adiabatic laser excitations. The analysis predictssuperradiant timescales in the idler emission in agreement with experimentalobservation. To relax the restriction of a single excitation, we develop adifferent theory of cascade emission, which is solved by numerical simulationof classical stochastic differential equation using the theory of open quantumsystems. The simulations are in good qualitative agreement with the analyticaltheory of superradiant timescales. We provide a quantum theory of near-infraredto telecom wavelength conversion in the diamond configuration. The systemprovides a crucial part of a quantum-repeater memory element, which enables a"stored" near-infrared photon to be converted to a telecom wavelength fortransmission without the destruction of light-atom quantum correlation.

Theory of light-matter interactions in cascade and diamond type atomic ensembles