Description
Book SynopsisClassical and Quantum Parametric Phenomena 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, topics such as nonlinear and stochastic dynamics, coupled systems, and quantum mechanics are introduced. Throughout the book, introductions are kept as succinct as possible and attention is focused on understanding parametric oscillators. As a result, the text helps readers to familiarize themselves 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. This book provides a resource for experimental and theoret
Trade ReviewIt is a good time to publish this book because the importance of parametric resonators is again growing reflecting the various practical applications. The included Python code is very nice and useful for the students who start to learn the detailed physics behind the theory. * Hiroshi Yamaguchi, NTT Basic Research Laboratories, Kanagawa *
The book is timely and will be appreciated by physicists working in different areas from condensed matter physics to quantum information, as well as people working in mechanical and electrical engineering. It will be used not only as a textbook, but also as a reference. * Mark Dykman, Michigan State University *
A fantastic addition to the literature. * Guillermo Villanueva, EPF Lausanne *
The book contains a cogent discussion of the different subjects in the context of exercises based on numerical Python codes; this will be especially useful for self-teaching. * Christian Brosseau, Optica Fellow and Professor of Physics, Université de Bretagne Occidentale, Brest, France *
Table of ContentsIntroduction 0.1: Historical Review 0.2: Present and Future 1 The Harmonic Resonator 1.1: Newton's Equation of Motion 1.2: Response of the Driven Resonator 1.3: Matrix Formulation 1.4: Parametric Modulation 1.5: Floquet Theory 1.6: Summary of Chapter 1 1.7: Exercises for Chapter 1 2 The Duffing Resonator 2.1: The Quartic Potential 2.2: The Cubic Potential 2.3: Summary of Chapter 2 2.4: Exercises for Chapter 2 3 Degenerate Parametric Pumping 3.1: The Nonlinear Parametric Resonator 3.2: Parametric Pumping via Three-Wave Mixing 3.3: Summary of Chapter 3 3.4: Exercises for Chapter 3 4 Dissipation and Force Fluctuations 4.1: The Role of Force Noise 4.2: The Fluctuation-Dissipation Theorem 4.3: The Probability Distribution Approach 4.4: Summary of Chapter 4 4.5: Exercises for Chapter 4 5 Parametric Resonators with Force Noise 5.1: Multistability and Quasi-Stable Solutions 5.2: Parametric Amplification Below Threshold 5.3: Parametric Pumping Above Threshold 5.4: Hierarchy of Relevant Timescales 5.5: Summary of Chapter 5 5.6: Exercises for Chapter 5 6 Coupled Harmonic Resonators 6.1: Static Coupling 6.2: Nondegenerate Three-Wave Mixing 6.3: Alternative Types of Coupling 6.4: Summary of Chapter 6 6.5: Exercises for Chapter 6 7 Coupled Parametric Oscillators 7.1: Equations for N Coupled Parametric Oscillators 7.2: Examples for N = 2 7.3: Networks with N > 2 7.4: Summary of Chapter 7 7.5: Exercises for Chapter 7 8 The Quantum Harmonic Oscillator 8.1: From Classical to Quantum Fluctuations 8.2: From First to Second Quantization 8.3: Quantum State Representations 8.4: Summary of Chapter 8 8.5: Exercises for Chapter 8 9 From Closed to Open Quantum Systems 9.1: Coupling to a Thermal Environment 9.2: The Driven Quantum Resonator 9.3: Summary of Chapter 9 9.4: Exercises for Chapter 9 10 The Quantum Parametric Oscillator 10.1: General Hamiltonian 10.2: Quantum Parametric Phenomena 10.3: Coupled Quantum Parametric Oscillators 10.4: Summary of Chapter 10 10.5: Exercises for Chapter 10 11 Experimental Systems 11.1: Mechanical Resonator Example 11.2: Electrical Resonator Example 11.3: Optical Resonator Example 11.4: Rescaling of the Numerical Values 11.5: Summary of Chapter 11 11.6: Exercises for Chapter 11 List of Important Symbols
