Search for Composite Dark Matter with Optically Levitated Sensors

Results are reported from a search for a class of composite dark matter models with feeble long-range interactions with normal matter. We search for impulses arising from passing dark matter particles by monitoring the mechanical motion of an optically levitated nanogram mass over the course of several days. Assuming such particles constitute the dominant component of dark matter, this search places upper limits on their interaction with neutrons of ${\alpha }_n\le 1.2\times {10}^{-7}$ at 95% confidence for dark matter masses between 1 and 10 TeV and mediator masses $m_{\varphi }\le 0.1\mathrm{eV}$. Because of the large enhancement of the cross section for dark matter to coherently scatter from a nanogram mass ($\sim {10}^{29}$ times that for a single neutron) and the ability to detect momentum transfers as small as $\sim 200\mathrm{MeV}/\mathrm{c}$, these results provide sensitivity to certain classes of composite dark matter models that substantially exceeds existing searches, including those employing kilogram- or ton-scale targets. Extensions of these techniques can enable directionally sensitive searches for a broad class of previously inaccessible heavy dark matter candidates.

Figure 1

Schematics of: (a) the levitated sphere and calibration electrodes, and (b) a DM nugget coherently scattering from a sphere via a light mediator, producing a momentum transfer $\overrightarrow{q}$. (c) Example 4.8 GeV impulse produced by applying a pulsed electric field at $t=0$ to a sphere with charge $-1e$. The raw waveform with minimal filtering (light, solid), filtered waveform (dark, solid), and filtered template (dashed) are shown for both in-loop and out-of-loop sensors (see text).

Figure 2

Measured rate of reconstructed impulses after all cuts (black points), compared to the spectrum with only live time selections applied (gray, solid) and with no cuts applied (gray, dashed). The Gaussian background (red, dotted), DM signal (blue, dot-dashed), and sum of background and signal (blue, solid) are also shown at the 95% C.L. upper limit, ${\alpha }_n=8.5\times {10}^{-8}$, for $M_X=5\times {10}^3\mathrm{GeV}$, $m_{\varphi }=0.1\mathrm{eV}$, and $f_X=1$. The inset shows the overall signal efficiency versus amplitude (black) and estimated error (gray band) above the analysis threshold, $q_{\mathrm{thr}}=0.15\mathrm{GeV}$ (dotted).

Figure 3

95% C.L. upper limits on the DM-neutron coupling ${\alpha }_n$ versus DM mass $M_X$ for several example values of mediator mass $m_{\varphi }$, assuming $f_X=1$.

Figure 4

Upper limits on the equivalent DM-neutron scattering cross section for a pointlike nugget ${\sigma }_{Xn}\equiv 4\pi {\alpha }_n^2{\mu }_{Xn}^2/q_0^4$ [60] versus $M_X$ for the model described in the text with $f_X=0.1$ (solid) and $f_X=1$ (dashed). Here ${\sigma }_{Xn}$ is evaluated for $m_d=1\mathrm{keV}$, $m_{\varphi }=0.1\mathrm{eV}$, and at a reference momentum of $q_0=m_n{v}_0$, where $m_n$ is the neutron mass and ${\mu }_{Xn}$ is the DM-neutron reduced mass. Model-dependent fifth-force constraints [48, 49] (dotted) are also shown, assuming $g_d\approx 1$. Because of sharp DM nugget form-factor suppression in the parameter space chosen here, existing detectors searching for $\mathrm{eV}\text{−}\mathrm{keV}$-scale NRs [62, 63, 64, 65, 66, 67, 68, 69] only constrain ${\sigma }_{Xn}\gg {10}^{-22}{\mathrm{cm}}^2$. The results reported here exceed even the projected sensitivity of a $\sim \mathrm{kilogram}\mathrm{year}$ exposure of an ambitious future detector with NR threshold as low as 1 meV (dot-dashed, see, e.g., [60, 70, 71, 72]). Cosmic microwave background limits on DM-baryon interactions assume a coupling to protons, which is model dependent and need not apply here [73], although the $f_X=1$ region is expected to be excluded by DM self-interaction bounds [60, 61], which do not apply for $f_X\lesssim 0.1$.