Introduction to Microwave Cavity Optomechanics
In this chapter, I introduce the concepts of electromechanical superconducting resonant circuits, a topic known as microwave cavity optomechanics. As part of that introduction, I will provide: a review of the field’s development, a discussion of its relat
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Introduction to Microwave Cavity Optomechanics Konrad W. Lehnert
Abstract In this chapter, I introduce the concepts of electromechanical superconducting resonant circuits, a topic known as microwave cavity optomechanics. As part of that introduction, I will provide: a review of the field’s development, a discussion of its relationship to “optical” cavity optomechanics, and a description of its current progress. In addition, I derive in pedagogical detail the classical dynamics of a mechanical oscillator parametrically coupled to a resonant circuit. Finally, I show that the cavity optomechanical Hamiltonian is the quantum description for a such an electromechanical circuit.
11.1 Introduction Microwave cavity optomechanics is the part of the field of nano- and microelectromechanics (NEMS and MEMS) that investigates the interaction between mechanical motion and electrical energy stored in microwave resonant circuits. It is one of the most promising strategies for observing and exploiting quantum behavior of macroscopic mechanical oscillators. The topic is the electrical analog of cavity optomechanics but has it roots in circuit quantum electrodynamics (cQED), the search for quantum effects in NEMS devices, and the effort to detect gravitational waves. The name microwave cavity optomechanics is a misnomer as the electrically resonant structures are not literally cavities but resonant circuits. The misnomer “cavity” persists to strengthen the analogy to cavity optomechanics and to resolve an ambiguity; the terms “resonator” and “oscillator” apply equally well to both the K. W. Lehnert (B) Department of Physics, University of Colorado, Boulder, CO, USA e-mail: [email protected] K. W. Lehnert JILA, National Institute of Standards and Technology, University of Colorado, Boulder, CO, USA
M. Aspelmeyer et al. (eds.), Cavity Optomechanics, Quantum Science and Technology, DOI: 10.1007/978-3-642-55312-7_11, © Springer-Verlag Berlin Heidelberg 2014
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mechanical and electrical degrees of freedom but “cavity” is understood to refer only to the electrical degree of freedom.
11.1.1 Relationship to Cavity Optomechanics The reemergence of interest in radiation pressure in optical cavities occurred because advances in microfabrication enabled the creation of high finesse optical cavities incorporating light and floppy mechanical oscillators [1–3]. This advent of cavity optomechanics sparked a new and vigorous effort to observe the quantum motion of a mechanical oscillator and the quantum nature of radiation pressure [4, 5]. A few years earlier, experiments with superconducting circuits had beautifully demonstrated the quantum nature of microwave light [6]. These experiments exploited superconducting microwave circuits to create artificial atoms (qubits) and cavities (superconducting resonators) and achieved coherent coupling between a single microwave photon and a qubit. It was natural to consider if the same sort of superconducting circuits could be used to create a strong interaction betwee
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