Annual-modulation fingerprint of the axion wind induced sideband triplet in quantum dot spin qubit sensors

TL;DR

The paper addresses laboratory searches for axion–electron couplings using phase-coherent silicon spin-qubit magnetometry. It models the axion dark matter field as a coherent oscillation and derives the resulting axion-induced effective magnetic field that drives electron spins, showing how adaptive coherent segmentation and narrowband readout preserve phase coherence within the axion coherence time. The key contribution is the identification of a parameter-free annual-modulation fingerprint—a baseband triplet at $\\{\\Omega_\\star,\\Omega_\\star \\pm\\Omega_\\oplus\\}$ with fixed spacing set by celestial mechanics—and its combination with high-frequency modulation sidebands to enable robust, dual signatures of axion wind, while accounting for Standard Halo Model linewidth and coherence. The results indicate that spin-qubit magnetometry can reach sensitivities to $g_{ae}$ in the range $\\sim 10^{-14}$–$10^{-10}$ for $m_a$ in the $1$–$10\\ \mu\\mathrm{eV}$ window, offering a complementary, scalable laboratory probe of axion–electron interactions and a framework adaptable to other spin-based sensors.

Abstract

We propose a phase-coherent, narrowband magnetometer for searching couplings between axions or axion-like particles (ALPs) and electron spins, using gate-defined silicon quantum-dot spin qubits. With repeated Ramsey echo sequences and dispersive readout, the qubit precession response can be tracked with sub-Hz spectral resolution. The accessible axion mass window is determined using a series of filtering protocols that take into account sensing noise, including readout errors and $1/f$ noise. We demonstrate clear evidence of sidereal modulation of the signal due to Earth's rotation, while Earth's orbital motion produces an annual amplitude envelope that generates sidebands at fixed frequency spacing $\pm Ω_\oplus$ around the sidereal component. For axion masses between $1$-$10~μ{\rm eV}$, the proposed method covers axion-electron coupling strengths $g_{ae}$ ranging from $10^{-14}$ to $10^{-10}$. Including both daily and annual modulation patterns in the likelihood analysis enhances the rejection of stationary or instrumental noise. Our results indicate that spin-qubit magnetometry can achieve sensitivities approaching those suggested by astrophysical considerations, providing a complementary, laboratory-based probe of axion-electron interactions. Although we focus on silicon spin-qubit architectures, the approach is broadly applicable to spin-based quantum sensors.

Figures (7)

• Figure 1: Relative motion of the Solar System and Earth. This is a demonstration of the relative motion to study the annual modulation of the axion signal. We consider the motion of the Solar System with respect to the Galactic rest frame as well as the orbital motion of the Earth around the Sun. The Solar System is assumed to move with a velocity of approximately $230$ km/s relative to the Galactic center, consistent with Standard Halo Model estimates. The Earth follows an approximately circular orbit around the Sun with velocity $30$ km/s. The Earth’s velocity vector changes direction over the course of a year, leading to an annual modulation in the net velocity relative to the Galactic dark matter halo. The effective axion wind observed in the laboratory frame varies periodically.
• Figure 2: Daily and annual envelope of the geometric modulation. Shown is the instantaneous daily series of $|\beta(t)|/\beta_0 = (v_{\rm lab}(t)/v_0)|\cos\theta(t)|$ over a full year (site latitude and sensor orientation as indicated in Table \ref{['Tab: Geom']}). The slow variation of the envelope follows the annual modulation at $\Omega_\oplus/2\pi \simeq 3.17\times10^{-8}\,\mathrm{Hz}$, while the rapid ripples are set by Earth’s sidereal rotation at $\Omega_\star/2\pi \simeq 1.1606\times10^{-5}\,\mathrm{Hz}$. Here $\beta_0$ fixes the overall scale (set by $g_{ae}\sqrt{2\rho_a}$ and a reference speed $v_0$).
• Figure 3: Daily RMS and its annual modulation (theory vs. noisy observations). For each sidereal day we compute $\mathrm{RMS}\{\beta(t)/\beta_0\}$ and normalize it by the yearly mean (vertical axis). The solid curve shows the geometry-only prediction; Orange circles denote simulated noisy observations generated with Pauli spin blockade type readout and simulated $1/f$, white, and random-telegraph noise. Green triangles indicate the Monte Carlo mean $\pm5\sigma$ from the same noise ensemble, and the blue solid line shows the geometry-only theoretical prediction. The slow envelope oscillates at the annual frequency $\Omega_\oplus/2\pi \simeq 3.17\times10^{-8}\,\mathrm{Hz}$ and fixes the sideband-to-carrier amplitude ratio of the $\Omega_\star\pm\Omega_\oplus$ triplet [Eq. (\ref{['Eq: triplet_time']})], namely $\epsilon_\oplus/2$. Note that the normalization uses a reference $\beta_0$ (set by $v_0$), so values may exceed unity when $v_{\rm lab}>v_0$.
• Figure 4: Baseband power spectral density and the annual-splitting triplet. PSD around the sidereal line at $\Omega_\star$ exhibits a triplet at $\{\Omega_\star,\ \Omega_\star \pm \Omega_\oplus\}$ produced by annual amplitude modulation of the daily component. Green dashed line marks $\Omega_\star$; red dashed lines mark $\Omega_\star \pm \Omega_\oplus$. The simulated precision $\delta f_W=7.93\times10^{-9}$Hz is the finite simulation resolution and windowing of the estimator; ideally the separation equals $\Omega_\oplus/2\pi\simeq3.17\times10^{-8}$ Hz. The vertical scale is in arbitrary units per Hz; see text for the estimator (Welch/taper) and dwell time.
• Figure 5: Axion–electron coupling sensitivity including geometric enhancements. Shaded areas indicate the detectable regions for the current and future configurations, while the band shows the DFSZ model range with the $\tan\beta=1$ benchmark curve. Three lower-edge curves are overlaid: the baseline limit (single axis, uniform weighting), the limit with matched weighting to daily/annual modulation, and the limit with matched weighting plus three-axis readout.