A mechanical oscillator coupled to the optical field in a cavity is a typical cavity optomechanical system. In our textbook, we prepare to introduce the quantum optical properties of optomechanical system, i.e. linear and nonlinear effects. Some quantum optical devices based on optomechanical system are also presented in the monograph, such as the Kerr modulator, quantum optical transistor, optomechanical mass sensor, and so on. But most importantly, we extend the idea of typical optomechanical system to coupled mechanical resonator system and demonstrate that the combined two-level structure and resonator system can serve as a generalized optomechanical system. The quantum optical properties, which exist in typical system, are also presented in the combined two-level structure and resonator system.

Quantum effects in macroscopic systems have long been a fascination for researchers. Over the past decade mechanical oscillators have emerged as a leading system of choice for many such experiments. The work reported in this thesis investigates the effects of the radiation-pressure force of light on macroscopic mechanical structures. The basic system studied is a mechanical oscillator that is highly reflective and part of an optical resonator. It interacts with the optical cavity mode via the radiation-pressure force. Both the dynamics of the mechanical oscillation and the properties of the light field are modified through this interaction. The experiments use quantum optical tools (such as homodyning and down-conversion) with the goal of ultimately showing quantum behavior of the mechanical center of mass motion. Of particular value are the detailed descriptions of several novel experiments that pave the way towards this goal and are already shaping the field of quantum optomechanics, in particular optomechanical laser cooling and strong optomechanical coupling.

To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.

This thesis presents experimental research on the interaction between the optical field and the mechanical oscillator in whispering-gallery mode microcavities. It demonstrates how optomechanical interactions in a microresonator can be used to achieve non-magnetic non-reciprocity and develop all-optically controlled non-reciprocal multifunctional photonic devices. The thesis also discusses the interaction between the travelling optical and mechanical whispering-gallery modes, paving the way for non-reciprocal light storage as a coherent, circulating acoustic wave with a lifetime of up to tens of microseconds. Lastly, the thesis presents a high-frequency phase-sensitive heterodyne vibrometer, operating up to 10 GHz, which can be used for the high-resolution, non-invasive mapping of the vibration patterns of acoustic devices. The results presented here show that optomechanical devices hold great potential in the field of information processing.

This thesis demonstrates the potential of two platforms to explore experimentally the emerging field of quantum thermodynamics that has remained mostly theoretical so far. It proposes methods to define and measure work in the quantum regime. The most important part of the thesis focuses on hybrid optomechanical devices, evidencing that they are proper candidates to measure directly the fluctuations of work and the corresponding fluctuation theorem. Such devices could also give rise to the observation of mechanical lasing and cooling, based on mechanisms similar to a heat engine. The final part of the thesis studies how quantum coherence can improve work extraction in superconducting circuits. All the proposals greatly clarify the concept of work since they are based on measurable quantities in state of the art devices.

During the last few years cavity-optomechanics has emerged as a new field of research. This highly interdisciplinary field studies the interaction between micro and nano mechanical systems and light. Possible applications range from novel high-bandwidth mechanical sensing devices through the generation of squeezed optical or mechanical states to even tests of quantum theory itself. This is one of the first books in this relatively young field. It is aimed at scientists, engineers and students who want to obtain a concise introduction to the state of the art in the field of cavity optomechanics. It is valuable to researchers in nano science, quantum optics, quantum information, gravitational wave detection and other cutting edge fields. Possible applications include biological sensing, frequency comb applications, silicon photonics etc. The technical content will be accessible to those who have familiarity with basic undergraduate physics.

The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.