A superconducting LC resonator in a multi-tesla magnetic field for tabletop kHz gravitational-wave detection

Abstract

We present a concept for a superconducting inductance--capacitance (LC) resonator immersed in a magnetic field for gravitational-wave detection in the kHz band. In the long-wavelength limit, a gravitational wave in a static magnetic field induces an oscillating magnetic-field perturbation proportional to the static magnetic field applied to the resonator and to the gravitational-wave strain. We show that a superconducting pickup circuit can convert this perturbation into a flux signal read out by a superconducting quantum interference device (SQUID)-based or quantum-limited amplifier chain. Inspired by resonant-mass detectors, we develop a three-loop coupled-circuit model and derive the equivalent strain-noise spectrum, including thermal noise, SQUID backaction, and measurement imprecision. Prototype measurements demonstrate a quality factor of $Q\simeq 5\times 10^5$, while $Q=10^7$ is considered as a future development target. Under the assumed flux coupling and an idealized quantum-limited SQUID noise model, optimized circuits yield projected strain sensitivities of order $10^{-21}\,\mathrm{Hz}^{-1/2}$ over $100\,\mathrm{Hz}$ bands in the $1$--$20\,\mathrm{kHz}$ range. Increasing the active high-field volume and improving quantum-limited readout could enable further sensitivity gains. This compact, tunable detector concept could complement interferometric gravitational-wave searches and motivate investigations of high-frequency astrophysical sources.