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(Color online) (a) MBE-deposited Al with no pre-deposition substrate cleaning yields a rough Al surface, shown in the AFM surface scan with 25 Å RMS roughness and (inset) a diffuse polycrystalline RHEED pattern, compared to (b) MBE-deposited Al with an 850 °C anneal in , with a much smoother film (4 Å RMS roughness) with sharply streaked RHEED. (c) x-ray diffraction scans of sputtered and MBE-grown films. Vertical scale corresponds to sputtered sample, with other samples plotted on same scale but vertically offset for clarity. All samples display substrate peaks and an Al(111) diffraction peak.
(Color online) (a) Measured normalized transmission magnitude and phase (colored squares), with a fit to Eq. (3) (solid black line) which yields GHz, and . The resonator had a m center stripline width and was patterned from an MBE-deposited Al film on a sapphire substrate that was annealed at 850 °C in . The data were taken at 50mK at low power with in the resonator. (b) Circuit diagram including mismatched complex impedances and for the transmission line input and output, includes the resonator and its coupling capacitance to the transmission line, which has characteristic impedance . (c) Parametric plot and fit of Im vs. Re of the same data and fit as (a). Points in the frequency range between the dashed lines (green squares) in (a) correspond to the points to the right of the dashed line in (c).
(Color online) Power dependence of the internal quality factor versus average photon number in the resonator , for resonators with m. Lines are guides to the eye. The typical low-power statistical error from a least-squares fit of Eq. (3) is %, smaller than the symbol size.
Sample process information; w is the resonator center stripline width, is the resonant frequency, and -H and -L are the internal quality factors at high power (before over-saturation) and low power (), respectively.
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