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.