Searching for dilaton dark matter with atomic clocks

We propose an experiment to search for ultralight scalar dark matter (DM) with dilatonic interactions. Such couplings can arise for the dilaton as well as for moduli and axion-like particles in the presence of $CP$ violation. Ultralight dilaton DM acts as a background field that can cause tiny but coherent oscillations in Standard Model parameters such as the fine-structure constant and the proton-electron mass ratio. These minute variations can be detected through precise frequency comparisons of atomic clocks. Our experiment extends current searches for drifts in fundamental constants to the well-motivated high-frequency regime. Our proposed setups can probe scalars lighter than $10^{-15}\mathrm{eV}$ with a discovery potential of dilatonic couplings as weak as $10^{-11}$ times the strength of gravity, improving current equivalence principle bounds by up to 8 orders of magnitude. We point out potential $10^4$ sensitivity enhancements with future optical and nuclear clocks, as well as possible signatures in gravitational-wave detectors. Finally, we discuss cosmological constraints and astrophysical hints of ultralight scalar DM, and show they are complimentary to and compatible with the parameter range accessible to our proposed laboratory experiments.

Figure 1

Diagrams of the (a) time and (b) frequency domains of a femtosecond laser with a time-evolving carrier-envelope phase ${\varphi }_{\mathrm{ce}}$, repetition rate $f_{\text{rep}}$, and carrier frequency $f_{\mathrm{c}}$. The comb in (b) is a Fourier transform of the pulse train in (a). In practice, $f_{\mathrm{c}}/f_{\text{rep}}\sim 10^6$ but here we have taken it to be $\mathcal{O}(10)$ for illustrative purposes.

Figure 2

Experimental setup of a frequency comparison of two optical lines. One clock laser is based on a “red” transition $f_{\mathrm{A}}$ and another is based on a “blue” transition $f_{\mathrm{B}}$. Light from both clock lasers is superposed with that from a frequency comb. Measurement of the beat frequencies $f_{b,\mathrm{A}}$ and $f_{b,\mathrm{B}}$, and comb frequencies $f_0$ and $f_{\text{rep}}$, provides the necessary information for a frequency ratio measurement.

Figure 3

Sensitivity to $d_g$ as a function of the scalar dark matter mass $m_{\varphi }=2\pi f_{\varphi }$ with the microwave-optical clock comparison experiment described in the text, for ${\tau }_{\mathrm{int}}=10^6,10^8\mathrm{s}$ (thin blue, thick blue), assuming $\varphi$ makes up all of the local dark matter. Regions excluded by composition-dependent (CD EP) and -independent (CI EP) equivalence principle tests are colored in red and orange, respectively, assuming $d_g\gg d_{m_i},d_e$.

Figure 4

Sensitivity to $d_{\widehat{m}}$ as a function of the scalar dark matter mass $m_{\varphi }=2\pi f_{\varphi }$ with the microwave-optical clock comparison experiment, assuming $d_{\widehat{m}}\gg d_g,d_e,d_{m_e}$. The green region depicts allowed scalar couplings of the QCD axion as in Eq. (4). Plot labels are similar to Fig. 3.

Figure 5

Sensitivity to $d_{m_e}$ as a function of the scalar dark matter mass $m_{\varphi }=2\pi f_{\varphi }$ with the microwave-optical clock comparison experiment, assuming $d_{m_e}\gg d_{m_i},d_e,d_g$. Plot labels are similar to Fig. 3.

Figure 6

Sensitivity to $d_e$ as a function of the scalar dark matter mass $m_{\varphi }=2\pi f_{\varphi }$ with the optical-optical clock comparison experiment described in the text, for ${\tau }_{\mathrm{int}}=10^6,10^8\mathrm{s}$ (thin blue, thick blue), assuming $\varphi$ makes up all of the local dark matter. Regions excluded by CD EP and CI EP tests are colored in red and orange, respectively, assuming $d_e\gg d_{m_i},d_g$. The green region depicts allowed scalar couplings of the QCD axion.

Figure 7

Same as in Fig. 4, but now including the reach on $d_{\widehat{m}}$ with a future nuclear-optical clock comparison after ${\tau }_{\mathrm{int}}={10}^8\mathrm{s}$. The future $d_{\widehat{m}}$ sensitivity of the composition-dependent EP test in Ref. [51] is shown as a dashed red line.

Figure 8

Same as in Fig. 6, but now including the reach on $d_e$ with a future nuclear-optical clock comparison after ${\tau }_{\mathrm{int}}={10}^8\mathrm{s}$. The future $d_e$ sensitivity of the composition-dependent EP test in Ref. [51] is shown as a dashed red line.

Figure 9

Same as in Fig. 3, but now including the reach on $d_g$ with a future nuclear-optical clock comparison after ${\tau }_{\mathrm{int}}={10}^8\mathrm{s}$. The estimated sensitivity to $d_g$ with current and proposed gravitational-wave detectors is also depicted: LIGO (brown), Advanced LIGO (dashed brown), AGIS-Future (dashed purple), and eLISA (dashed gray).

Figure 10

Cosmological and astrophysical constraints in the $m_{\varphi }-|{\lambda }_{\varphi }^{\text{eff}}|$ plane. Structure formation constraints are indicated in dark and light gray. Superradiance (SR) bounds from observations of supermassive black holes are depicted as the two leftmost yellow regions, while the bounds from observations of stellar-mass black holes are depicted as the rightmost yellow region. For reference, we include the effective quartic contribution generated for $\varphi$ when $d_{m_t}\sim {10}^{-6}$ from SM corrections (blue), the gravitational contribution to the effective quartic for a massive scalar field (black), as well as the mass-quartic relation for the QCD axion (green). The structure formation bounds assume ${\rho }_{\varphi }\sim {\rho }_{\mathrm{DM}}$, and disappear when ${\rho }_{\varphi }\lesssim {10}^{-1}{\rho }_{\mathrm{DM}}$.