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Fabrication procedure for VGCs. (a) Lower VGC plate patterned from an Al layer 100 nm thick on a sapphire wafer. (b) Patterned sacrificial layer (Nb, Si, or ) 200 nm thick with “via” holes. (c) Al top capacitor plate, 100 nm thick, is sputtered and patterned on top of the sacrificial layer. Al fills the “via” holes in the sacrificial layer, forming posts that support the top plate. The lower plate is connected to the ground plane. (d) The sacrificial layer is removed by an isotropic high-pressure plasma etch through the holes in the top plate.
(a) SEM micrograph of a fabricated resonator incorporating a VGC and a gradiometric multicoil inductor with VGXs. The resonator is coupled to a CPW transmission line through an IDC and surrounded by a perforated ground plane. (b) Magnified part of the VGC where the gap between the top and bottom plates is visible. (c) Magnified part of the inductor showing VGXs. (d) Square VGC with Nb posts (previously developed) in parallel with a Josephson junction as a part of a phase qubit.
Measurement set-up to test resonators with (a) one or (b) two . Microwave drive is attenuated by 20 dB at 4 K and then by 20 dB at 50 mK before the input port 1 (not shown), which ensures a thermal population of much less than one photon in the resonator. (c) SEM micrograph of a fabricated circuit with five different resonators each connected through a to a single CPW transmission line. (d) Transmitted signal of a similar circuit with equal design values, and values staggered to produce a frequency separation between the resonance dips of .
(a) Transmitted signal of an resonator with a large VGC (1 mm across and ). The data show a single resonance peak at and no higher-order resonant modes. The inset shows typical data with a fitted Lorentzian peak for a double- circuit containing a VGC and VGXs. (b) Capacitance vs VGC plate overlap area. (c) Measured vs for three capacitors with dielectric materials (, Si, or ) between the plates, a VGC with Al posts, and an IDC capacitor, all measured with double- circuits. (d) Spectroscopy of the phase qubit incorporating a VGC. The inset shows energy relaxation from the qubit excited state with characteristic time .
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