Tunable High Q Superconducting Microwave Resonator

We have developed a frequency tuning system for a ``lumped-element'' thin-film superconducting Nb microwave resonator on sapphire intended for coupling to cold trapped $^{87}$Rb atoms. $^{87}$Rb has hyperfine ground states, $|^{5}S_{1/2},F=1\rangle$ and $|^{5}S_{1/2},F=2\rangle$, which are separated by about 6.83 GHz and available as a two-level system for a qubit. The resonator consists of a meandering inductor and an interdigitated capacitor coupled to a transmission line. At \emph{T}=12 mK and on resonance at 6.863 GHz, the loaded quality factor is 40,000. We employ an Al pin as a frequency tuner by placing it above the inductor using a piezo stage so that one can effectively change the inductance of the resonator.