Exclusion Limits on Hidden-Photon Dark Matter near 2 neV from a
  Fixed-Frequency Superconducting Lumped-Element Resonator
  We present the design and performance of a simple fixed-frequency
superconducting lumped-element resonator developed for axion and hidden photon
dark matter detection. A rectangular NbTi inductor was coupled to a Nb-coated
sapphire capacitor and immersed in liquid helium within a superconducting
shield. The resonator was transformer-coupled to a DC SQUID for readout. We
measured a quality factor of $\sim$40,000 at the resonant frequency of 492.027
kHz and set a simple exclusion limit on $\sim$2 neV hidden photons with kinetic
mixing angle $\varepsilon\gtrsim1.5\times10^{-9}$ based on 5.14 hours of
integrated noise. This test device informs the development of the Dark Matter
Radio, a tunable superconducting lumped-element resonator which will search for
axions and hidden photons over the 100 Hz to 300 MHz frequency range.
