| In this thesis, we develop and experimentally verify a theoretical formalism of spontaneous parametric down-conversion (SPDC) by considering a multidimensional representation for the two-photon quantum state, which can be concurrently entangled in frequency, wave vector, and polarization. The second-order nonlinear-optical process of spontaneous parametric down-conversion generates pairs of photons that exhibit nonclassical correlations, when a laser beam, conventionally referred to as the pump, impinges on a nonlinear crystal. This process can be viewed as the decay (or conversion) of an energetic pump photon into two less energetic photons, conventionally referred to as the signal and the idler. Quantum interference is studied as a signature of the nonclassical correlations of the generated photon pairs that reveal the properties of the two-photon quantum state. The interplay among frequency, wave vector, and polarization parameters in quantum-interferometric measurements sheds light on the inconsistencies between the conventional theory and the recent experimental results in ultrafast SPDC. We also investigate theoretically and experimentally the effects of the intervening optical system on quantum interference. We further extend our formalism to include photon-pair generation in media with inhomogeneous distributions of second-order nonlinearity. As a special case, we explore the interference effects arising from SPDC that is collectively generated in two spatially separated macroscopic generation media. This is experimentally realized using two bulk crystals that are positioned sequentially in the path of the pump beam. The polarization quantum-interference pattern is found to have its origin in two mechanisms: chromatic dispersion of the medium between the crystals, and spatiotemporal effects that arise from the inclusion of transverse wave vectors of the down-converted photons. These effects, in turn, provide two concomitant avenues for controlling the spatiotemporal properties of the two-photon quantum state generated in SPDC. We further propose a novel design for a generation medium that may serve to generate two-photon states that possess joint entanglement in frequency and polarization. The approach presented here facilitates the application of such quantum states to appropriate quantum-information schemes and quantum technologies. |
