Thin-film superconducting resonator tunable to the ground-state hyperfine splitting of $^{87}$Rb

TL;DR

This paper presents a superconducting Nb microwave resonator precisely tunable to the hyperfine transition frequency of rubidium-87, achieved through coarse lithography adjustments and fine piezoelectric tuning at millikelvin temperatures.

Contribution

It introduces a superconducting resonator with high-precision tunability to match atomic hyperfine transitions, combining lithography and piezoelectric methods for fine control.

Findings

Achieved a tuning range of 18 MHz.

Demonstrated fine frequency adjustment of 8.7 kHz per piezo step.

Resonator tuned within 0.3 ppm of $^{87}$Rb hyperfine splitting.

Abstract

We describe a thin-film superconducting Nb microwave resonator, tunable to within 0.3 ppm of the hyperfine splitting of $^{87}$Rb 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 \emph{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.