Classical and Quantum Parametric Phenomena

Abstract This book provides an overview of the phenomena arising when parametric pumping is applied to oscillators. These phenomena include parametric amplification, noise squeezing, spontaneous symmetry breaking, activated switching, cat states, and synthetic Ising spin lattices. To understand these effects, we introduce topics such as nonlinear and stochastic dynamics, coupled systems, and quantum mechanics. Throughout the book, we keep these introductions as succinct as possible and focus our attention on understanding parametric oscillators. As a result, we familiarize ourselves with many aspects of parametric systems and understand the common theoretical origin of nanomechanical sensors, optical amplifiers, and superconducting qubits. Parametric phenomena have enabled important scientific breakthroughs over the last decades and are still at the focus of intense research efforts. Our intention is to provide a resource for experimental and theoretical physicists entering the field or wishing to gain a deeper understanding of the underlying connections. As such, we combine formal and intuitive explanations, accompanied by exercises based on numerical python codes. This combination allows the reader to experience parametric phenomena from various directions and apply their understanding directly to their own research projects. For lecturers, the book supplies all the material necessary for an advanced class on the topic.