Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO Dynamics

Broadly speaking, this thesis is about nonlinear optics, quantum mechanics, and computing. More specifically, it covers four main topics: Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO Dynamics. Tying them all together is a theory of open quantum systems called the SLH model, which I introduce in Chapters 1-2. The SLH model is a general framework for open quantum systems that interact through bosonic fields, and is the basis for the quantum circuit theory developed in the text. Coherent LQG control is discussed in Chapters 3-4, where I demonstrate that coherent feedback outperforms measurement-based feedback for certain linear quadratic-Gaussian (LQG) problems, and explain the discrepancy by the former's simultaneous utilization of both light quadratures. Semiclassical truncated-Wigner techniques for quantum-optical networks are discussed in Chapter 5, leading to a thorough discussion of quantum noise in systems with free-carrier nonlinearities (Chapter 6), comparison to the Kerr nonlinearity, and potential applications for analog computing based on limit cycles and amplification (Chapters 7-8). Ising machines based on optical parametric oscillators (OPOs) are discussed in Chapters 9-10, the former focusing on large 1D and 2D networks of OPOs, and the latter on the dynamics of a single OPO in the ultrafast, synchronously-pumped regime. Optical properties and design considerations for silicon photonic waveguides are are treated in Chapter 11.