| dc.description.abstract | This thesis is a study of the quantum properties of multimode entangled photons created by spontaneous parametric down-conversion. More specifically, we attempt to utilize this multimode character in quantum information tasks such as Bell-state measurement and the generation of photons entangled in transverse spatial degrees of freedom.As a first investigation, a theoretical study of multimode Hong-Ou-Mandel interference was conducted. It is shown that the fourth-order interference effects depend upon the transverse spatial properties of the biphoton. Due to the transfer of the angular spectrum of the pump beam to the biphoton state shown by Monken et al. [Phys. Rev. A 57 3123 (1998)], the parity of the pump beam can be used as a control parameter of fourth-order interference. A Hong-Ou-Mandel interference experiment was performed using first-order Hermite-Gaussian pump beams. The experimental results show that the observed fourth-order interference behavior depends upon the parity of the pump beam. A first application of multimode interference in quantum information is in optical Bell-state analysis, which uses fourth-order interference techniques. A technical difficulty encountered with previous methods of Bell-state analysis is the requirement that the detectors be sensitive to photon number. However, using multimode interference, Bell-state analysis can be performed using single-photon detectors. To show that multimode interference could be used to improve upon these schemes, a simple Bellstate measurement experiment using multimode polarization entangled-photons was performed. Three classes of Bell-states were identified in the coincidence basis (with single photon detectors). In addition, similar methods for Bell-state analysis using hyperentangled states are discussed. Using multimode interference, we improve upon a previous proposal of Kwiat and Weinfurter [Phys. Rev. A 58 R2623 (1998)], which requires photons entangled in more than one degree of freedom. Finally, we propose a new method of Bell-state analysis of hyperentangled photons that does not require detectors sensitive to photon number and can be implemented non-locally. As a further study of the multimode properties of down-converted photons, we investigate the conservation of orbital angular momentum in spontaneous parametric down-conversion. It is well known that a light field can carry orbital angular momentum in the form of an azimuthal phase dependence. We show theoretically that the angular spectrum transfer enables the generation of photons entangled in orbital angular momentum. A simple multimode fourth-order interference experiment was performed which confirms these theoretical predictions. Finally, we studied the generation of photons entangled in Hermite-Gaussian modes. Using the theory of angular spectrum transfer, we show that spontaneous parametric down-conversion generates photons entangled in Hermite-Gaussian modes and calculate the probability amplitude to generate arbitrary Hermite-Gaussian modes. In addition we discuss the generation of maximally entangled Bell-states and arbitrary bipartite pure states. | |
