Fluctuating Nonlinear Oscillators From Nanomechanics to Quantum Superconducting Circuits

The book provides a unifying insight into fluctuation phenomena in a broad variety of vibrational systems of current interest. It consists of individual chapters written by leading experts in the field. The chapters are self-contained and complement each other. The ongoing rapid development of well-characterized mesoscopic vibrational systems has made it possible to address fundamental physics problems and to explore new approaches to quantum and classical measurements, with applications to quantum information, condensed matter physics, and engineering. The book gives an account of major results in this direction. The topics include dynamics and quantum control of microcavity modes coupled to qubits, measurements with bifurcation-based amplifiers and new types of such amplifiers; switching rate scaling and new quantum mechanisms of metastable decay; wave mixing and parametric excitation in the quantum regime; collective phenomena and the interaction-induced discrete time symmetry breaking; and back-action and shot noise in electron-vibrational systems.

1. Circuit quantum electrodynamics with a nonlinear resonator. 2. Quantum-classical correspondence for a dc-biased cavity resonator-Cooper-pair transistor system. 3. Activated switching in nonlinear micromechanical resonators. 4. Measurement and control of quantum cavities with electronic atoms. 5. Non-degenerate three wave mixing with Josephson junctions. 6. Dynamics of nano-magnetic oscillators. 7. Periodically modulated quantum nonlinear oscillators. 8. Nonlinear oscillators and high fidelity qubit state measurement in circuit quantum electrodynamics. 9. Spontaneous time-symmetry breaking in a vibrating cold atom system. 10. Nonlinear nanoelectromechanical systems. 11. Collective dynamics in arrays of coupled nonlinear resonators. 12. Carbon nanotubes: Nonlinear high-Q resonators with strong coupling to single-electron tunneling. 13. Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators. 14. Dynamical bifurcation and amplification in Josephson junction oscillators. 15. Parametric oscillators based on superconducting circuits.

Mark Dykman is Professor of Physics at Michigan State University.