We describe the fabrication and measurement of microwave coplanar waveguideresonators with internal quality factors above 10 million at high microwavepowers and over 1 million at low powers, with the best low power resultsapproaching 2 million, corresponding to ~1 photon in the resonator. Thesequality factors are achieved by controllably producing very smooth and cleaninterfaces between the resonators' aluminum metallization and the underlyingsingle crystal sapphire substrate. Additionally, we describe a method foranalyzing the resonator microwave response, with which we can directlydetermine the internal quality factor and frequency of a resonator embedded inan imperfect measurement circuit.
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