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 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.
KeywordsJosephson Junction Microwave Pulse Mechanical Resonator Resonant Response Energy Relaxation Time
We would like to thank J. M. Martinis for invaluable experimental support, M. Geller for numerous conversations and calculations, and A. Berube for assistance with resonator fabrication and measurements. The entire membership of the UC Santa Barbara phase qubit group assisted enormously in this experiment and in providing and maintaining the experimental infrastructure. This work was supported by the US National Science Foundation (NSF) under grant DMR-0605818 and by the Intelligence Advanced Research Projects Activity under grant W911NF-04-1-0204. Devices were made at the University of California, Santa Barbara, Nanofabrication Facility, which is part of the NSF-funded US National Nanotechnology Infrastructure Network.
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