Searching for scalar field dark matter with hyperfine transitions in alkali atoms

Fundamental constants such as masses and coupling constants of elementary particles can have small temporal and spatial variations in the scalar field dark-matter model. These variations entail time oscillations of other constants, such as the Bohr and nuclear magnetons, Bohr radius, and the hyperfine structure constant. In the presence of an external magnetic field, these oscillations induce hyperfine transitions in atoms and molecules. We determine the probability of magnetic dipole hyperfine transitions, caused by the oscillating fundamental constants, and propose an experiment that could detect the scalar field dark matter through this effect. This experiment may be sensitive to the scalar field and axion dark matter with mass in the range $1\mathit{\mu }\mathrm{eV}<m<100\mathit{\mu }\mathrm{eV}$.

Figure 1

Sketch of the experimental protocol of the resonant dark-matter detector based on cold atoms.

Figure 2

(a) Projected sensitivity of the atomic hyperfine transition experiment to the combined coupling constant ${\mathrm{\Lambda }}_{A\mu }$ estimated with the use of Eq. (38) assuming the integration time $t_{\text{integ}}=10\mathrm{s}$, number of atoms $N_{\text{at}}={10}^{10}$, and number of repetitions at each frequency bin $N_{\mathrm{rep}}={10}^4$. With these parameters, it is possible to scan a relatively narrow interval $\mathrm{\Delta }\omega ={10}^{-4}\omega$ within four months. By setting $N_{\mathrm{rep}}=1$, the full frequency interval may be scanned within 1.5 yr with a reduced sensitivity by the factor ${10}^{-2}$. (a)–(d) represent also the sensitivity to the coupling constants ${\mathrm{\Lambda }}_p$, ${\mathrm{\Lambda }}_{\gamma }$, ${\mathrm{\Lambda }}_e$, and ${\mathrm{\Lambda }}_H$, respectively, with excluded regions colored in pink. In (b), we present also the existing limits from the ADMX experiment found in Ref. [25]. Note that $1\mathrm{\mu }\mathrm{eV}=2\pi \times 242\mathrm{MHz}$.

Figure 3

Sensitivity of the hyperfine transitions experiment to the axion-electron coupling constant $g_{aee}$ and its comparison with the results of the QUAX experiment [65].