A Study of Optical Nonlinearities at the Single-Photon Level for Quantum Logic

In this dissertation, we shall focus on theoretically studying quantum nonlinear optical schemes to construct a conditional phase gate at the single-photon level. With an aim to develop analytical models, we shall carry out a rigorous quantized multimode field analysis of some of these schemes involving only the interacting field operators. More specifically, we shall first study the three-wave mixing process involving two single-photons in a second-order nonlinear medium (x(2)) under two different cases viz. when the photons are traveling with equal velocities and when they are traveling with different velocities, and explore the possibility of using them for building a conditional phase phase gate. Finally, we shall study the interaction of single-photon wavepackets with a realistic atomic system viz. an ensemble of five-level atoms, to construct a phase gate. We will particularly look at the giant Kerr effect in electromagnetically induced transparency to explore the possibility of using this scheme for achieving a conditional phase shift and to understand how the bandwidth gets restricted naturally in such an atomic system