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Description of resonator devices. (a) Photomicrograph of a wrap-geometry resonator (circled) coupled to a qubit through a few femtofarad capacitor and a microwave drive through a sub femtofarad capacitor for measurement. Resonator for measurement is coupled to a second microwave drive through a sub femtofarad capacitor and disconnected from the qubit. (b) Illustrations (not to scale) of different geometries used for resonators. The total length of coplanar lines are all about 8.8 mm. (c) A straight resonator (circled) coupled to a qubit and a microwave drive for . Resonator for is coupled to a second microwave drive and disconnected from the qubit. (d) Cross-section of the coplanar resonator showing the center trace width , and the gap separation between the center trace and the ground plane.
(a) Plot of vs temperature at high excitation power for Re resonators with different center-trace widths , as indicated. (b) Fractional variations of the resonance frequency vs temperature for resonators shown in (a). The variation scales inversely with , characteristic of kinetic inductance. Inset shows the low temperature regime where a monotonic change of is observed down to the lowest temperature. Lines are guides to the eye.
(a) vs resonator voltage (with ) for Re resonators of different gap widths . Lines are fits to the data. (b) Same as (a), but for Al resonators. Note that for Al is systematically lower than for Re. (c) Results from a fit to a power-independent (diamonds) and power-dependent (squares), vs . Open (filled) symbols are for Re (Al). Corresponding trace width is shown on top scale. Solid lines are fits using from surface TLS loss. Dashed lines are guide to the eye.
(a) Normalized vs the applied cooling field for Re resonators of different trace widths . (b) Normalized vs the applied field, as measured with a qubit, for a Re resonator with and . Data for the resonator and qubit is shown. Lines are drawn as a guide to the eye.
Resonator parameters. The thickness of the metal films are 110–130 nm, and widths and were chosen to give a characteristic impedance, except for the resonator. is quoted at low power, , and is determined via qubit-resonator swap experiments.
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