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Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 157-164). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (BSc. (Hons))--Australian National University, 2002. / Available via the Australian National University Library Electronic Pre and Post Print Repository. Title from title screen (viewed Mar. 28, 2003). "A thesis submitted for the degree of Bachelor of Science in Physics, The Australian National University" Bibliography: p. 77-80.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Vita. Includes bibliographical references.

Thesis (M.S.)--Brigham Young University. Dept. of Physics and Astronomy, 2007. / Includes bibliographical references (p. 44-46).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisors: Qian Niu and Mark G. Raizen. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

The bright squeezed vacuum state of light is a macroscopic nonclassical state found at the output of a strongly pumped unseeded travelling-wave optical parametric amplifier. It has been applied to quantum imaging, quantum communication, and phase supersensitivity, to name a few. Bright squeezed states are in general highly multimode, while most applications require a single mode. We separated two nonlinear crystals in the direction of propagation of the pump in order to narrow the angular spectrum down to a nearly-single angular mode. We observed noise reduction in the photon number difference between the two down-converted channels, which constitutes of proof of nonclassicality. By introducing a dispersive medium between the two nonlinear crystals, we were able to tailor the frequency spectrum of bright squeezed vacuum and to dramatically reduce the number of frequency modes down to 1.82 ± 0.02, bringing us closer to truly single-mode bright squeezed vacuum.

Structured light has shown great promises and impacts in various fields such as microscopy, optical trapping, sensing, classical communication, high dimensional quantum information, quantum key distribution (QKD) and quantum metrology. In this Thesis, we will be discussing two projects, in the context of structured light, one about the stability of 3D optical topologies and the other about the reconstruction of strongly correlated bi-photon states. In the introduction, we will be reviewing some of the basic concepts needed to follow the two projects. Starting from the spatial modes and their characteristics, we discuss about some interferometric approaches to reconstruct the phase and the amplitude of an electromagnetic field, either for a classical laser beam or for photons. Moreover, we briefly explain the spontaneous parametric down conversion (SPDC) process that is commonly used for generating entangled bi-photon states. In the second chapter, after giving an overview about singular optics and optical topologies, we explore the effect of different types of aberrations on three different 3D optical structures, Trefoil knot, Cinquefoil knot and Hopf Link. In this work we show that these structures are robust under aberrations with the highest strength if the defining aperture of the aberration is big enough. In addition, we discuss about how these aberrations will modify the structure if we decrease the size of the aperture and in which aperture the structures start to break and therefore, we investigate the impact of the strength under such apertures. In the third chapter, we return to the SPDC process, discuss the thin-crystal approximation, spatial mode correlations of an entangled bi-photon state, and coincidence imaging performed with time stamping cameras. We propose an approach to characterize an unknown two-photon state using interference between the unknown bi-photon state and a reference bi-photon state in addition to coincidence imaging. We show that this approach is faster, scalable and loss-free compared to projective measurements. Finally, in the conclusion, we put together the results of these two projects and discuss about the future work that can follow up on what is done so far.