Axion Signal Search Using Hybrid Nuclear-Electronic Spin Systems

Abstract

Conventional nuclear magnetic resonance searches for the galactic axion wind lose sensitivity at low frequencies due to the unfavourable scaling of inductive readout. Here, we propose a hybrid architecture where the hyperfine interaction transduces axion-driven nuclear precession into a high-bandwidth electron-spin readout channel. We demonstrate analytically that this dispersive upconversion preserves the specific sidereal and annual modulation signatures required to distinguish dark matter signals from instrumental backgrounds. When instantiated in a silicon ${ }^{209} \text{Bi}$ donor platform, the hybrid sensor is projected to outperform direct nuclear detection by more than an order of magnitude over the $10^{-16}-10^{-6} \text{eV}$ wide mass range. With collective enhancement, the design reaches a $5 σ$ sensitivity to DFSZ axion-nucleon couplings within one year, establishing hyperfine-mediated sensing as a competitive path for compact, solid-state dark matter searches.

Figures (4)

• Figure 1: Schematic of a prototypical experimental design. A gate-defined electron spin qubit (left) provides a fast, high-bandwidth readout channel, while a donor nuclear spin (right) serves as the axion-sensitive element. Gates P1, P2, Q1, and Q2 define the confinement potentials and are shown for illustration. Realizations can follow electron- and hole-based architectures in Refs. Pla2014Muhonen2018Huang2019Hendrickx2021Liles2024Hendrickx2024Guangchong2025, with the donor nuclear spin acting as the probe of the axion wind field as in Refs. Gonzalez2021Veldhorst2014Veldhorst2015Maurand2016Cifuentes2024Steinacker2025.
• Figure 2: (a) Normalized electron filter functions $|F(\omega)|^2/\tau^2$ for Ramsey and Hahn echo versus normalized frequency $\xi = f\tau$; the Hahn sequence narrows the main lobe and shifts the first zero from $\xi \simeq 1$ (Ramsey) to $\xi \simeq 2$. (b) Nuclear toggling filter amplitude $|Y_N(\omega)|/\tau$ for Ramsey, Hahn, and CPMG with $N = 4, 8, 16$, exhibiting passbands centered near $\xi \simeq N$ with width $\sim 1/\tau$. This filter structure enables tunable frequency selectivity while preserving the sidereal modulation pattern, in contrast to conventional inductive NMR. Together these properties define the accessible mass-scan range.
• Figure 3: (a) Time-domain evolution of the electron rotating-frame longitudinal magnetization $\langle S_x(\tau)\rangle$ under continuous spin lock at a Rabi frequency $\Omega_R/2\pi = 50~\text{kHz}$. The axion-induced nuclear precession introduces a weak frequency modulation at $\omega_a/2\pi = 5~\text{kHz}$. (b) Power spectral density of the same signal, $|\tilde{S}_x(\omega)|^2$, showing the locked carrier at $\Omega_R/2\pi$ (black dashed line) and symmetric axion-induced sidebands at $\Omega_R/2\pi \pm \omega_a/2\pi$ (red dashed lines). These spectral sidebands represent the frequency-encoded axion response characteristic of spin-lock detection.
• Figure 4: Projected $5\sigma$ sensitivity to axion-nucleon couplings. Shown are the calculated discovery thresholds on $g_{aNN}$ for a ${}^{209}$Bi donor ensemble under several standard magnetometry protocols: Ramsey (Blue), Hahn-echo (Orange), XY8 (Green), and continuous spin-lock ($T_{1\rho}$) detection (Black). All curves include realistic device parameters and noise models (Supplementary Tables II–III), and assume collective enhancement from an entangled ensemble of $N=10^{6}$ nuclear spins together with resonator gain $G_{\text{res}}(Q{=}10^{5})$. The effective signal field entering each protocol is $B_{e,\text{eff}} = F_{\text{ent}}G_{\text{res}}G_{\text{hyb}}B_{a}^{(N)}$. The purple shaded region represents the spin-lock Monte-Carlo distribution (median and 5%-95% band), which provides the best sensitivity across most of the mass range. The yellow band denotes the DFSZ model predictions, and the horizontal magenta region indicates the current SN1987A cooling bounds (95% C.L.). Part of the parameter windows are created from Ref. AxionLimits.