Search for light scalar dark matter with atomic gravitational wave detectors

We show that gravitational wave detectors based on a type of atom interferometry are sensitive to ultralight scalar dark matter. Such dark matter can cause temporal oscillations in fundamental constants with a frequency set by the dark matter mass and amplitude determined by the local dark matter density. The result is a modulation of atomic transition energies. We point out a new time-domain signature of this effect in a type of gravitational wave detector that compares two spatially separated atom interferometers referenced by a common laser. Such a detector can improve on current searches for electron-mass or electric-charge modulus dark matter by up to 10 orders of magnitude in coupling, in a frequency band complementary to that of other proposals. It demonstrates that this class of atomic sensors is qualitatively different from other gravitational wave detectors, including those based on laser interferometry. By using atomic-clock-like interferometers, laser noise is mitigated with only a single baseline. These atomic sensors can thus detect scalar signals in addition to tensor signals.

Figure 1

Spacetime diagram of the light-pulse sequence on two atom interferometers, illustrated for $n=4$ (i.e., maximum four photon momenta transferred). A $\pi /2$ laser pulse (gray, wavy) splits the wave function of atoms both at $x_1$ and at $x_2$ into the ground state $|g⟩$ (blue, solid) and the excited state $|e⟩$ (red, dashed) with equal probabilities. Subsequent $\pi$ laser pulses (black, wavy) exchange $|g⟩\leftrightarrow |e⟩$ and typically only interact with one branch of each wave function due to Doppler shifts. A final $\pi /2$ pulse interferes the wave function of both interferometers. Interaction points are indicated by gray squares (black dots) for $\pi /2$ ($\pi$) pulses. For clarity, atomic separations are exaggerated; realistically, $x_1\sim x_1^{*}\sim L-x_2\sim L-x_2^{*}\ll L$.

Figure 2

Parameter space for the coupling $d_{m_e}$ to electrons (top panel) and $d_e$ to photons (bottom panel), as a function of dark matter mass $m_{\varphi }$. Blue curves depict the $\mathrm{SNR}=1$ sensitivity envelopes of the proposed atomic sensors: a terrestrial experiment operated in broadband mode (“AI-TB”); a long-baseline, broadband, space-based antenna (“AI-SB”); and a shorter, resonant satellite antenna (“AI-SR”). Also depicted are 95% C.L. constraints from searches for new Yukawa forces that violate/conserve the equivalence principle (“$\mathrm{EP}/5\mathrm{F}$”, gray regions) [32, 33, 34], atomic spectroscopy data in Dy and in $\mathrm{Rb}/\mathrm{Cs}$ (light and dark purple regions) [10, 11], seismic data on the fundamental breathing mode of Earth (red) [35], and a search for acoustic excitations in the AURIGA resonant-mass detector (red band) [36]. Green regions show natural parameter space for a 10-TeV cutoff, and allowed parameter space for the QCD axion.

Figure 3

Parameter space for the Higgs portal coupling $b$ as a function of dark matter mass $m_{\varphi }$. Curves and regions are as in Fig. 2. Here, the green region highlights couplings $b$ for which the lightest physical mass eigenvalue $m_{\varphi }$ of the scalar potential is natural at the classical level, as described in the text. Loop-level quantum corrections to the mass are subdominant, so the natural region is independent of the UV cutoff.