Searching for axion dark matter with magnetic resonance force microscopy

TL;DR

The paper targets ultralight dark matter in the GHz Compton-frequency regime, focusing on axions that couple derivatively to electrons to produce an oscillating effective magnetic field $B_{\rm eff}$ at frequency $\\omega_{\\rm DM}=m_{\\rm DM} c^2/\\hbar$. It proposes a magnetic resonance force microscopy (MRFM) approach where electron spins polarized by a DC field interact with a micromagnet; a pump field $B_{\\rm p}$ amplifies the DM signal and down-converts it to the mechanical resonance frequency $\\omega_m=|\\omega_{\\rm DM}-\\omega_{\\rm p}|$, yielding a spin-dependent force detected optically. A noise model shows that, with current technology, a minute-long integration can reach sensitivities competitive with laboratory axion searches, and the method can scan the axion mass by varying the pump frequency $\\omega_{\\rm p}$ and the bias field $B_0$. The scheme also extends to constraints on other dark-matter–Standard Model couplings, including dark photons and axion-photon interactions, and supports multiplexing and scaling (e.g., multiple YIG spheres or dilution refrigerator operation).

Abstract

We propose a magnetic resonance force microscopy (MRFM) search for axion dark matter around 1 GHz. The experiment leverages the axion's derivative coupling to electrons, which induces an effective A.C. magnetic field on a sample of electron spins polarized by a D.C. magnetic field and a micromagnet. A second pump field at a nearby frequency enhances the signal, with the detuning matched to the resonant frequency of a magnet-loaded mechanical oscillator. The resulting spin-dependent force is detected with hih sensitivity via optical interferometry. Accounting for the relevant noise sources, we show that current technology can be used to put constraints competitive with those from laboratory experiments with just a minute of integration time. Furthermore, varying the pump field frequency and D.C. magnetic field allows one to scan the axion mass. Finally, we explore this setup's capability to put constraints on other dark matter - Standard Model couplings.

Figures (5)

• Figure 1: Diagram of the MRFM setup. The top illustrates the general scenario where a magnetized sample under the influence of a D.C. field $B_0\hat{z}$ and a field due to a nearby micromagnet attached to a mechanical resonator undergoes magnetic resonance electron spins in the presence of a dark matter induced magnetic field $B_{\rm DM}\cos(\omega_{\rm DM} t)$. All the spins within the resonance region put a force on the resonator. A pump field $B_{\rm p}\cos(\omega_{\rm p} t)$ parallel to the $B_{\rm DM}$ amplifies the dark matter signal and modulates it down to the micromagnet-loaded resonator's resonance frequency $\vert\omega_{\rm DM}-\omega_{\rm p} \vert=\omega_{\rm m}$, inducing vibrations that are read out optically. The bottom shows the two mechanical systems considered in this work: membranes and cantilevers.
• Figure 2: Sensitivity plot of axion-electron coupling strength $g_{aee}$ as a function of axion mass $m_{\rm DM}$ (lower axis) and corresponding Compton frequency $f_{\rm DM}$ (top axis). A second y-axis gives the strength of the effective magnetic field induced on electrons by axions corresponding to the coupling strength $g_{aee}$. Our results for MRFM based axion search are given in red and blue for a membrane and cantilever, respectively. For each resonator, a 100 day long run at a single frequency is shown as well as a 100 day scan of minute long runs at neighboring frequencies, showing that one can choose to increase sensitivity or bandwidth. The QCD axion band is shown in yellow and existing constraints from astrophysical capozzi2020axion, space gondolo2009solaraprile2022search and laboratory experiments terrano2015shortyan2019constraining are shown in gray. Also shown are narrowband constraints from other magnetic resonance based searches in green, labeled QUAX crescini2018operationcrescini2020axion, UWA flower2019broadening and QND ikeda2022axion. The top right panel shows the finer details of a single sensitivity line including the two sidebands at $\omega_p\pm\omega_m$. The bottom right panel shows the contributions from the back action noise (purple), thermal noise (yellow), and imprecision noise (green) to the total noise equivalent force (red).
• Figure 3: Sensitivity plot of dark photon kinetic coupling parameter $\epsilon$ as a function of dark photon mass $m_{\rm DM}$ (lower axis) and corresponding Compton frequency $f_{\rm DM}$ (upper axis). Our results for MRFM based axion search are given in red and blue for a membrane and cantilever, respectively. For each resonator, a 100 day long run at a single frequency is shown as well as a 100 day scan of minute long runs at neighboring frequencies, showing that one can choose to increase sensitivity or bandwidth. The gray region represents constraints from astrophysical and cosmological observations assuming the dark photon makes up majority of dark matter, while dark green and light green are constraints from haloscope searches and rescaled limits from axion searches. See caputo2021dark for details of various constraints on the dark photon kinetic coupling.
• Figure 4: The magnetic field gradient produced by the resonator-attached micromagnet (shown as a red dot at the origin) is plotted as a contour against distance. The yellow region denotes the sensitive slice that is determined by the magnetic resonance condition $B_0+B_z = \frac{\omega_L(\vec{r})}{\gamma}$ and the linewidth $1/T_2$. The red circles depict a $3\times3$ grid of YIG spheres.
• Figure 5: Noise contributions to the mechanical resonator motion due to back action noise (yellow), thermal noise (red), and imprecision noise (blue) are shown as the square root of the noise equivalent force spectral density as a function of frequency. The dominant part of the noise equivalent force (NEF), shown in black, is imprecision noise off-resonance and thermal noise on-resonance with the mechanical frequency $f_m$. The box on the lower left shows the zoomed in region around $f_m$. The bandwidth of the setup can be seen to be around $100~\rm Hz$.