Dark Matter Nuclear Magnetic Resonance is Sensitive to Dark Photons and the Axion-Photon Coupling

We demonstrate that nuclear magnetic resonance based searches for dark matter (DM) have intrinsic and powerful sensitivity to dark photons and the axion-photon coupling. The reason is conceptually straightforward. An instrument such as CASPEr-Gradient begins with a large sample of nuclear spins polarised in a background magnetic field. In the presence of axion DM coupled to nucleons, the spin ensemble feels an effective magnetic field $\mathbf{B}\propto \mathrm{\nabla }a$ that tilts the spins, generating a potentially observable precession. If the magnetic field is real rather than effective, the system responds identically. A real field can be generated by a kinetically mixed dark photon within the shielded region the sample is placed or an axion coupled to photons through its interaction with the background magnetic field. We show that all three signals are detectable and distinguishable. If CASPEr-Gradient were to reach the QCD axion prediction of the axion-nucleon coupling, it would simultaneously be sensitive to kinetic mixings of $\epsilon \simeq 3\times {10}^{-16}$ and axion-photon couplings of $g_{a\gamma \gamma }\simeq 2\times {10}^{-16}{\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}$ for $m\simeq 1\mu \mathrm{e}\mathrm{V}$.