Microwave-Frequency Mechanical Resonators Operated in the Quantum Limit
In this chapter, we describe an experiment in which the quantum ground state of one vibrational mode of a mechanical resonator was reached when the structure was cooled in a dilution refrigerator to \(T \sim 25\) mK. The resonator had a fundamental dilat
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Microwave-Frequency Mechanical Resonators Operated in the Quantum Limit Aaron O’Connell and Andrew N. Cleland
Abstract In this chapter, we describe an experiment in which the quantum ground state of one vibrational mode of a mechanical resonator was reached when the structure was cooled in a dilution refrigerator to T ∼ 25 mK. The resonator had a fundamental dilatational resonance frequency in excess of 6 GHz, so once cooled to this temperature, the number of thermal phonons at this frequency is vanishingly small. This achievement is a direct consequence of the high resonance frequencies obtainable with the class of mechanical resonator used in the experiment, which is known as a film bulk acoustic resonator, or FBAR. In this chapter, we begin by briefly describing the mechanics of bulk acoustic resonance and FBAR structures, and we present a simple electrical circuit model for the resonator. Experiments using this type of mechanical resonator in the classical regime are then described. We then introduce the Josephson phase quantum bit (qubit), a device which forms the heart of the measurement scheme used to probe the mechanical resonator in the quantum regime, and describe the coupling mechanism between the qubit and a mechanical resonator. Lastly, we present experimental measurements of the resonator in the quantum regime, where the qubit was used to both prepare and measure non-classical mechanical states in the resonator.
12.1 Film Bulk Acoustic Resonators Film bulk acoustic resonators are dilatational-mode mechanical resonators fabricated using piezoelectric materials. Voltages applied to metal electrodes placed on the opposing surfaces of the resonator generate piezoelectric strain, either dilating or contracting the volume of the resonator. When the applied voltage oscillates at a frequency corresponding to a natural mechanical resonance of the structure, large A. O’Connell · A. N. Cleland (B) University of California, Santa Barbara, CA, USA e-mail: [email protected] M. Aspelmeyer et al. (eds.), Cavity Optomechanics, Quantum Science and Technology, DOI: 10.1007/978-3-642-55312-7_12, © Springer-Verlag Berlin Heidelberg 2014
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Fig. 12.1 Film bulk acoustic resonator geometry, piezoelectric response, and model circuit representation. a Idealized geometry of a mechanical resonator, comprising a piezoelectric material of thickness d with infinitely thin metal plates, or electrodes, on both the top and bottom surfaces. b Sketch illustrating the dilatational response of the piezoelectric structure to an externally-imposed voltage, which generates an electric field between the electrodes; light gray indicates metal electrodes, while dark gray represents piezoelectric material. The thickness dimension is grossly exaggerated for illustrative purposes, and the metal electrodes are shown here with non-zero thickness. c Equivalent electrical circuit model for mechanical response near the fundamental dilatatio
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