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Thin-film superconducting resonator tunable to the ground-state hyperfine splitting of 87Rb
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Image of FIG. 1.

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FIG. 1.

(a) Optical image of lumped-element microwave resonator coupled to a transmission line and surrounded by ground plane. Gray regions are Nb and black regions are sapphire. (b) Optical image of Al pad added to Nb interdigitated capacitor.

Image of FIG. 2.

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FIG. 2.

(a) Schematic of Al pin and piezoelectric translation stage tuning system. (b) Schematic of experimental set-up. Microwaves from port 1 of the vector network analyzer (VNA) are sent to the resonator on the mixing chamber through microwave lines and cold attenuators. After the resonator the signal passes through two isolators, is amplified by low noise amplifiers (LNAs) at 3.6 K and 300 K, and travels back to port 2 of the VNA. (c) Simulated resonance frequency f r versus the fraction of a finger in the interdigitated capacitor.

Image of FIG. 3.

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FIG. 3.

(a) Measured ratio of transmitted to input power (P out /P in ) versus frequency after coarse tuning. (b) Deviation of the resonance frequency f r from f 0 = 6.827815 GHz versus time over 70 hours. Time required to measure each point was about 2 minutes.

Image of FIG. 4.

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FIG. 4.

(a) Shift of measured (red circles) and simulated (blue squares) resonance frequency f r around 87Rb hyperfine splitting frequency f Rb versus distance between Al pin and resonator. (b) f r - f Rb versus number N of piezo steps at different piezo step voltages. (c) and (d) are detailed views of (b) at step voltages of 36 V and 30 V, respectively. (e) and (f) show extracted internal quality factor Q i and external quality factor Q e versus tuned frequency f r for different input power P in , respectively. Black dashed line shows the 87Rb hyperfine splitting frequency f Rb .

Image of FIG. 5.

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FIG. 5.

(a) Internal quality factor Q i and (b) external quality factor Q e of the second resonator plotted versus tuned frequency f r for different input power P in . Black dashed line shows the 87Rb hyperfine splitting frequency f Rb . The input power to this Al resonator was about -100.5 dBm, which corresponds to about 60,000 photons.


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We describe a thin-filmsuperconductingNbmicrowaveresonator, tunable to within 0.3 ppm of the hyperfine splitting of 87Rb at f Rb = 6.834683 GHz. We coarsely tuned the resonator using electron-beam lithography, decreasing the resonance frequency from 6.8637 GHz to 6.8278 GHz. For in situ fine tuning at 15 mK, the resonator inductance was varied using a piezoelectric stage to move a superconducting pin above the resonator. We found a maximum frequency shift of about 8.7 kHz per 60-nm piezoelectric step and a tuning range of 18 MHz.


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Scitation: Thin-film superconducting resonator tunable to the ground-state hyperfine splitting of 87Rb