High-Q Superconducting Lumped-Element Resonators for Low-Mass Axion Searches

TL;DR

The study addresses the challenge of enabling high-sensitivity searches for low-mass axions by developing a high-Q, fixed-frequency lumped-element superconducting resonator near 250 kHz. The authors design, assemble, and characterize a ~1 L inductor-capacitor resonator with an unprecedented unloaded quality factor $Q_{ m ul} \approx 2.1\times10^{6}$ at $T \approx 315~\mathrm{mK}$, achieved through ultralow-loss materials, careful joint preparation, and robust magnetic shielding. A ringdown-based measurement protocol demonstrates stable, reproducible $Q$ values across cryogenic cycles, with a measured $R_{ m ul} \approx 0.572~\mathrm{m}\Omega$ and a mean resonance frequency around $f_0 \approx 2.49656\times10^{5}$ Hz. The work provides practical design guidelines and demonstrates the potential of lumped-element resonators to boost scan rates in low-mass axion searches, outlining future directions including deeper cryogenic cooling, alternative materials, SQUID readout integration, and tunable frequency control.

Abstract

Low-frequency superconducting lumped-element resonators have recently attracted significant attention in the context of axion dark matter searches. Here we present the design and implementation of a fixed-frequency superconducting resonator operating near $250~\mathrm{kHz}$, possessing an inductor volume of $\sim 1$ liter and achieving an unloaded quality factor $Q \approx 2.1\times10^{6}$. This resonator represents a significant improvement over the state of the art and informs the design of searches for low-mass axions.

Figures (9)

• Figure 1: Principal circuit of the resonator with injection and readout lines. A room-temperature function generator applies an input voltage $V_{\mathrm{in}}$ to the injection line, carrying current $I_{\mathrm{in}}$. The injection coil is inductively coupled to the resonator coil through mutual inductance $M_{\mathrm{in}}$, injecting the signal into the resonator at cryogenic temperature ($\approx 315$ mK). The resonator itself consists of an inductor ($L$) and capacitor ($C$), with an unloaded (residual) resistance $R_\mathrm{ul}$ that represents internal losses. The output signal is extracted by a readout coil, coupled to the resonator via mutual inductance $M_{\mathrm{out}}$, producing a current $I_{\mathrm{out}}$ that travels out of the cryostat and is converted into a voltage $V_{\mathrm{out}}$ by a room-temperature amplifier. The input and output impedances are $Z_{\mathrm{in}}$ and $Z_{\mathrm{out}}$, while the self-inductances of the injection and readout coils are $L_{\mathrm{in}}$ and $L_{\mathrm{out}}$.
• Figure 2: CAD cross section of the resonator apparatus. The dimensions are in millimeters. The top cap (1) encloses screw terminals (2) where the injection and readout lines transition from copper wire (outside the shield) to NbTi (inside). The capacitor (3) is mounted to the ceiling of the capacitor chamber. An intermediate set of screw terminals (4) on a mounting plate inside the capacitor chamber provides a convenient break for the injection and readout lines. The inductor coil (5) is positioned centrally within the inductor chamber and is connected to the capacitor with NbTi leads. A high-purity 5N (99.999%) aluminum shield (6) surrounds the assembly and defines three chambers: capacitor, inductor, and a SQUID chamber reserved for future integration.
• Figure 3: Photograph of the resonator apparatus. The resonator is mounted on a two-level copper table comprising an upper and a lower copper plate. The upper plate is thermally anchored to the bottom of the $^3$He pot, while the lower plate is anchored to the bottom of the $^4$He pot of the $^3$He-$^4$He sorption refrigerator. The assembly is mounted to the $4\,\mathrm{K}$ stage via G-10 support legs; carbon-fiber legs support the upper plate. A passive pyrolytic graphite heat switch thermally links the two plates. The lower copper plate is also coupled to the $4\,\mathrm{K}$ stage through a second passive pyrolytic-graphite heat switch.
• Figure 4: CAD model of the inductor coil assembly. Dimensions are in millimeters. Four sapphire rods (1) join the opposing Al 1100 side frames (2) and serve as winding mandrels for the NbTi wire. The frames are fastened with Al 6061 studs and nuts (3). Al 1100 square nuts (4) secure the ends of a threaded Al 1100 tie rod (6) that clamps the side plates to stiffen the structure. The rod is held in tension and is the only element holding the two ends together. Sapphire washers under the coil (5) provide electrical isolation from the chassis to avoid closed superconducting loops. Each coil's leg carries an Al 6061 flanged-button screw (7) paired with two sapphire washers (8) to anchor the NbTi wire. Two of these screw-washer sets form the injection and readout loops by routing the wire around one sapphire rod, while the remaining two sets terminate the winding. The completed assembly is mounted on an Al 1100 baseplate (9).
• Figure 5: Photograph of the inductor coil mounted inside the high-purity (5N) aluminum resonator shield. When superconducting, the shield expels magnetic field (Meissner effect), screening the flux and thereby lowering the coil’s effective self-inductance.