| In this dissertation, a new method of quantum state tomography (QST) for light is presented and demonstrated. This QST approach characterizes the transverse-spatial state of an ensemble of single photons by measuring the transverse-spatial Wigner function of the ensemble. The first experimental measurements of the full transverse-spatial state at the single-photon level for light are presented. To perform these measurements, we developed a novel photon-counting, parity-inverting Sagnac interferometer.; We also show how this method may be generalized to determine the transverse-spatial state of an ensemble of photon pairs, which may be entangled. This allows characterization of the continuous-variable entanglement properties that can arise in photon-pair states. The method introduced measures the two-photon, transverse-spatial Wigner function, which may be used to demonstrate a Bell-inequality violation.; In treating photons as particle-like entities, as we do in the interpretation of these experiments, the question of the most appropriate theoretical description comes to the fore. In order to describe these experiments, we extend a quantum theory of light called photon wave mechanics, based on a single-particle viewpoint, and we show it to be equivalent to the standard quantum field theory of light. We show that the wave mechanics for multi-photon states is identical to the evolution of the coherence matrices that appear in classical, vector coherence theory. The connection between classical coherence theory (CCT) and photon wave mechanics allows us to utilize the well-developed tools of CCT to describe the propagation of multi-photon states. We present two example calculations to show the utility of the photon wave mechanics treatment. |
