Nonlinear Dynamics in Quantum Photonic Structures
Quantum optics unites physical optics and the quantum field theory of light. A fundamental consequence of light-field quantization is the appearance of vacuum fluctuations, or quantum noise, which has no classical analogue and stems from the Heisenberg uncertainty relations. Nonlinear optical interactions "on a chip" offer new, unexplored functionalities, and may play a key role in future technologies. In this respect, a major theoretical and computational challenge is the development of new, tractable models of the nonlinear quantum dynamics in realistic devices with complex geometries in multiple dimensions. Description of nonlinear pulse propagation, interaction, and localization phenomena in multiple dimensions requires dipole coupling to at least a 2D resonant medium, whereby the electric field of a single-photon excitation is coupled to at least two distinct dipole optical transitions. The chapter applies the vector Maxwell-pseudospin formalism to the problem of nonlinear optical pulse propagation in planar waveguides and microcavities with embedded quantum systems.