Broad frequency tuning of a Nb$_{3}$Sn superconducting microwave cavity for dark matter searches

Abstract

We demonstrate a novel broad-frequency tuning mechanism for superconducting microwave cavities designed for dark matter searches. Using a Nb$_3$Sn-coated cigar-shaped cavity operating at approximately 9\,GHz, we achieve continuous frequency tuning exceeding 1\,GHz by mechanically separating the two cavity halves: a "tuning-by-opening" technique. Finite-element method simulations predict that radiative losses do not degrade the quality factor even for large openings, as a closed cavity with an intrinsic quality factor of $10^7$ maintains this value for apertures up to 9\,mm, corresponding to a tuning range from 9.0 to 7.5\,GHz. Experimental validation using both copper ring spacers and a continuous sliding mechanism confirms $Q_0$ values exceeding the dark matter quality factor across the entire explored frequency range, despite mechanical imperfections and film non-uniformities. This tuning approach avoids inserting elements into the resonant volume, making it particularly suitable for high-Q superconducting cavities in axion haloscope experiments and readily applicable to REBCO-based implementations capable of operating in multi-tesla magnetic fields.

Figures (6)

• Figure 1: (a) Top view of one semi-cell and cavity cross section, with dimensions, in mm, along the relevant axes. The parts in red are copper spacers used to separate the two cavity halves. The lateral plates are colored in light gray, while the cigar-shaped inner surface is shown in darker gray. (b) TM$_{010}$ electric field mode profile obtained with FEM Simulations in the open configuration (6 mm-gap). (c) Side view of the open cavity with 6 mm gap. Sensor S measures the temperature of cavity half 1 thermalized to cavity half 2 through 4 copper spacers. Cavity half 2 is in direct contact with the copper cold finger.
• Figure 2: (a) Experimental setup. The cryogenic parts at approximately $4\,$K are the cavity, a circulator and a HEMT amplifier. A room-temperature switch routs the VNA output either to the weakly coupled antenna C2 for transmission measurement $S_{21}$ (b) or to the circulator port for measuring the reflection $S_{22}$ at the coupler C1 (c). In (b) and (c) data are fitted using Eqs. \ref{['eq:1']} and \ref{['eq:2']}, respectively. In both plots the resonant frequency $f_{\mathrm{c}} = 8.996217\,$GHz has been subtracted from the x‑axis. (d) Unloaded quality factor $Q_0$ measured at different temperatures below $T_C$, extracted by fitting the magnitude of the reflection function. The pink curve given by Eq. \ref{['eq:7']} fits the data for $T < T_C/2$. At low temperatures, the residual resistance $R_0$ dominates over the BCS resistance $R_{\mathrm{BCS}}$, which is exponentially suppressed. The reported $R_0$ is obtained from the fit. The light blue curve is obtained from surface resistance calculations based on BCS theory. The two-fluid model for the superconducting state Halbritter:1974 is used with the following parameters: energy gap $\Delta/k_\mathrm{B} \,T_\mathrm{C} = 2.06$, critical temperature $T_\mathrm{C} = 17.8\,$K, London penetration depth $\lambda_\mathrm{L} = 40\,$nm, coherence length $\xi_0 = 20\,$nm, and residual resistance ratio $\mathrm{RRR} = 1.74$.
• Figure 3: Simulation results. (a) TM$_{010}$ mode resonant frequency $f_\mathrm{c}$ (blue dots) and effective cavity volume (red dots) as function of gap size. (b) Unloaded quality factor $Q_0$ for different gap widths (green/orange dots), obtained by assigning finite/perfect conductivity to both the inner surface and lateral plates of the cavity. The chosen finite value of conductivity is $10^3$ times the copper conductivity at LHe temperature ($\sigma_{\mathrm{Cu}}^{4\mathrm{K}} = 3.2 \times 10^8\,$S/m). Computed (brown dots) intrinsic quality factor $(1/Q_0 - 1/Q_{\mathrm{leak}})^{-1}$ .
• Figure 4: Impact of misalignments between the two cavity halves on $Q_0$. In the FEM simulations we consider both (a) the possible lateral misalignment $x$ relative to the parallel configuration and (b) the effect of a rotation angle $\phi$, as depicted in the insets.
• Figure 5: (a) Tuning slope of the resonant frequency obtained using copper spacers corresponding to several gap widths; the closed-cavity value is also included. The linear fit yields a tuning slope of $188\,\mathrm{MHz/mm}$. (b) Unloaded quality factor $Q_0$ extracted from reflection measurements performed with spacers (red circles). The green diamonds and blue squares correspond to measurements obtained with the continuous tuning system, with the green dataset derived from the cavity decay time constant measured using the pulsed RF method at selected frequencies and the blue dataset obtained with a VNA. The pulsed RF method enables characterization even when the pulse tube (PT) is operating. The errors assigned to each measurement is not visible since it is within the symbols