CASPER: Axion Dark Matter NMR Search

• CASPER is an NMR-based experiment that searches for dark-matter axions and axion-like particles via their coupling to nuclear spins within a sensitive mass range below 10⁻⁶ eV.
• The experiment exploits axion-induced oscillatory nuclear electric dipole moments interacting with strong electric and magnetic fields to generate a measurable spin precession signal.
• Advanced sample materials, polarization techniques, and precision magnetometry combine in CASPER to probe axion parameter space beyond traditional photon-coupling searches.

CASPER refers to the Cosmic Axion Spin Precession Experiment, a nuclear magnetic resonance (NMR)–based precision instrumentation program designed to detect dark-matter axions and axion-like particles (ALPs) via their predicted coupling to nuclear spins. The CASPEr project targets the theoretically well-motivated QCD axion, a pseudoscalar field postulated both as a solution to the Strong-CP Problem and as a natural dark matter candidate, as well as a broad class of ultralight ALPs. By exploiting axion-induced nuclear electric dipole moments (EDMs) and their resulting spin precession in bulk samples under strong electric and magnetic fields, CASPEr seeks to access axion parameter space not probed by photon-coupling (microwave cavity) searches and to ultimately cover masses $m_a \lesssim 10^{-6}\ \mathrm{eV}$ with coupling down to $g_{aNN}\sim 10^{-9}$–$10^{-8}~\mathrm{GeV}^{-1}$, thereby opening a path to exploring high-$f_a$ (low-$m_a$) QCD axions and ALP dark matter (Budker et al., 2013, Kimball et al., 2017, Garcon et al., 2017).

1. Theoretical Mechanism and Signal Generation

The underlying physics involves two main axion-sector couplings: to gluons and to nucleons. For the QCD axion $a$ (or a general ALP), the relevant effective Lagrangian terms are

$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$

where $f_a$ is the axion decay constant and $g_{aNN}$ is the derivative axion–nucleon coupling. In a classical, oscillating axion background $a(t) = a_0\cos(m_a t)$ established by the galactic dark-matter field, the gluonic term induces a time-varying effective QCD $g_{aNN}\sim 10^{-9}$0-angle: $g_{aNN}\sim 10^{-9}$1 leading to an oscillating neutron EDM,

$g_{aNN}\sim 10^{-9}$2

where $g_{aNN}\sim 10^{-9}$3 is determined by the local dark-matter density $g_{aNN}\sim 10^{-9}$4.

Equivalently, the derivative nucleon coupling yields, by the nucleon equation of motion, an effective pseudoscalar interaction $g_{aNN}\sim 10^{-9}$5 with $g_{aNN}\sim 10^{-9}$6 and $g_{aNN}\sim 10^{-9}$7. Both couplings result in oscillatory EDMs aligned along the nuclear spin.

Key physical assumptions are: (1) the axion field is spatially coherent on laboratory scales, oscillating with frequency $g_{aNN}\sim 10^{-9}$8 and coherence time $g_{aNN}\sim 10^{-9}$9; and (2) static EDM systematics are suppressed by confining the search to a narrow spectral band around $10^{-8}~\mathrm{GeV}^{-1}$0, which itself is scanned by scanning the laboratory field.

2. NMR Detection Principle and Signal Derivation

In practice, a solid-state sample with a large intrinsic electric field $10^{-8}~\mathrm{GeV}^{-1}$1 is placed in a static magnetic field $10^{-8}~\mathrm{GeV}^{-1}$2 (defining the nuclear quantization axis). The axion-induced, oscillating EDM

$10^{-8}~\mathrm{GeV}^{-1}$3

interacts with $10^{-8}~\mathrm{GeV}^{-1}$4 to yield an oscillating Hamiltonian

$10^{-8}~\mathrm{GeV}^{-1}$5

which acts as a transverse “effective” magnetic field in the frame defined by $10^{-8}~\mathrm{GeV}^{-1}$6, causing nuclear spin precession at instantaneous Rabi frequency

$10^{-8}~\mathrm{GeV}^{-1}$7

where $10^{-8}~\mathrm{GeV}^{-1}$8 is the nuclear magnetic moment. On resonance (i.e., $10^{-8}~\mathrm{GeV}^{-1}$9), this causes coherent build-up of transverse nuclear magnetization over the smaller of the axion coherence time $f_a$0 and the ensemble transverse relaxation time $f_a$1.

The observable is the growth of transverse magnetization,

$f_a$2

where $f_a$3 is the nuclear number density, $f_a$4 is the nuclear polarization, and $f_a$5 is the Schiff suppression factor characteristic of heavy nuclei.

3. Experimental Implementation

3.1 Sample and Material Choice

• Sample: High-$f_a$6 ferroelectric crystals (e.g., PbTiO$f_a$7 enriched in $f_a$8Pb, spin-1/2) are utilized to maximize the Schiff moment and effective internal electric field. Number density of order $f_a$9, with Schiff suppression $m_a$0–$m_a$1.
• Polarization: Achievable polarizations $m_a$2 at $m_a$3, $m_a$4 (Phase 1), and up to $m_a$5 using optical pumping (Phase 2).
• Electric Field: Internal $m_a$6 V/cm at the heavy nucleus site, due to broken inversion symmetry.

3.2 Signal Readout and Magnetometry

• Detection: Nuclear spins are polarized along $m_a$7, precession is induced if $m_a$8 has a transverse component. The Larmor frequency $m_a$9 is swept to scan for resonance with $a$0.
• Magnetometer: Transverse magnetization is detected as an oscillating magnetic field using precision magnetometers: SQUIDs ($a$1 T/$a$2), or, in future phases, SERF atomic magnetometers ($a$3 T/$a$4).
• Sample Volume: $a$5 cm$a$6 is envisaged for high SNR, with $a$7 up to 100 s possible via dynamical decoupling.

4. Sensitivity, Parameter Coverage, and Projected Reach

The experiment’s reach is characterized in the $a$8 plane, with sensitivity ultimately determined by achievable polarization, $a$9, sample volume, magnetometer noise, and scan time.

Phase	$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$0	Pol. $$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$1	$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$2	Sensitivity $$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$3	$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$4 covered	Features
Phase 1	≤10 T	$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$5	1 ms	$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$6–$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$7 GeV$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$8	$$\mathcal{L} \supset (a/f_a)\, (\alpha_s/8\pi)\, G^a_{\mu\nu} \tilde{G}^{a\mu\nu} + g_{aNN} (\partial_\mu a) \bar{N}\gamma^\mu\gamma^5 N,$$9–$f_a$0 eV	3yr scan, transverse magnetiz.
Phase 2	≤20 T	$f_a$1	1 s	$f_a$2 GeV$f_a$3	$f_a$4–$f_a$5 eV	Optical pumping, long $f_a$6
Magnetization-noise limit	—	$f_a$7	100 s	$f_a$8–$f_a$9 GeV$g_{aNN}$0	$g_{aNN}$1–$g_{aNN}$2 eV	Dynamical decoupling

• CASPEr uniquely probes $g_{aNN}$3 eV and can achieve $g_{aNN}$4 GeV (QCD axion, $g_{aNN}$5 eV), well beyond exclusion from SN1987A and static EDM bounds, and orthogonally to cavity searches such as ADMX, which probe axion–photon coupling at higher masses (Budker et al., 2013).

5. Systematic Effects, Backgrounds, and Technical Challenges

• Magnetic Noise: Suppressed with superconducting and magnetic shields (%%%%79$g_{aNN}\sim 10^{-9}$380%%%% attenuation), differential sample geometry, field subtraction, and careful shielded magnet design.
• Mechanical Vibration: Rigid mounting, isolation, and post-measurement correction.
• Spin-Projection Noise: Fundamental quantum limit, reduced by increasing sample volume and maximizing $g_{aNN}$8.
• Relaxation Time $g_{aNN}$9: Extended by decoupling or magic-angle spinning; chemical-shift and dipolar broadening are managed accordingly.
• Electric Field Stability: Internal $a(t) = a_0\cos(m_a t)$0 is static; dissipation, heating, and field-reversal systematics common to static-EDM searches are absent.
• Low-Frequency Sensitivity: For $a(t) = a_0\cos(m_a t)$1 eV, resonance broadens, and a “DC” non-resonant readout tracking oscillating EDMs via Fourier analysis is applicable up to $a(t) = a_0\cos(m_a t)$2kHz.

6. Significance and Context within Dark Matter Searches

CASPEr, by exploiting the axion’s unique coupling to nuclear moments, covers parameter space inaccessible to photon-coupling experiments and complements astrophysical limits. It is able to scan orders of magnitude in $a(t) = a_0\cos(m_a t)$3 beyond those reached by supernova (SN1987A) neutrino bounds or static-EDM measurements, and is positioned to either detect or significantly constrain high-$a(t) = a_0\cos(m_a t)$4 QCD axions and broad-band ALP dark matter.

CASPEr’s NMR-based method is orthogonal to optical and resonance-cavity techniques and leverages state-of-the-art developments in precision quantum-magnetometry and condensed matter for dark-matter physics (Budker et al., 2013, Kimball et al., 2017, Garcon et al., 2017).