Searching for Vector Dark Matter with an Optomechanical Accelerometer

We consider using optomechanical accelerometers as resonant detectors for ultralight dark matter. As a concrete example, we describe a detector based on a silicon nitride membrane fixed to a beryllium mirror, forming an optical cavity. The use of different materials gives access to forces proportional to baryon ($B$) and lepton ($L$) charge, which are believed to be coupling channels for vector dark matter particles (“dark photons”). The cavity meanwhile provides access to quantum-limited displacement measurements. For a centimeter-scale membrane precooled to 10 mK, we argue that sensitivity to vector $B-L$ dark matter can exceed that of the Eöt-Wash experiment in integration times of minutes, over a fractional bandwidth of $\sim 0.1\%$ near 10 kHz (corresponding to a particle mass of ${10}^{-10}\mathrm{eV}/{\mathrm{c}}^2$). Our analysis can be translated to alternative systems, such as levitated particles, and suggests the possibility of a new generation of tabletop experiments.

Figure 1

Concept for an optomechanical accelerometer sensitive to vector $B$ or $B-L$ ultralight dark matter. (a) Lumped-mass model. (b) Membrane-mirror example. Colors represent masses (materials) with different $B$ or $B-L$ charge (charge density), $q_i$ (${\rho }_i$).

Figure 2

Centimeter-scale ${\mathrm{Si}}_3{\mathrm{N}}_4$ membranes as vector $B-L$ dark matter detectors. Dashed gray and solid blue curves are models for the acceleration sensitivity of four different membranes, expressed as a minimum $B-L$ coupling strength $g_{B-L}$ [Eq. (12)], for a measurement time equal to the DM coherence time (${\tau }_{\mathrm{DM}}=2Q_{\mathrm{DM}}/{\omega }_{\mathrm{DM}}$) and one year, respectively. Each model assumes a mechanical quality factor of $Q_0={10}^9$, an operating temperature of $T=10\mathrm{mK}$, a displacement sensitivity of $2\times {10}^{-17}\mathrm{m}/\sqrt{\mathrm{Hz}}$, and a suppression factor of $f_{12}=0.05$ relative to a Be reference mass. A full multimode spectrum for the 20 cm membrane is shown in green. Pink, red, and blue regions are bounds set by the Eöt-Wash experiments, LIGO, and MICROSCOPE, respectively. At right, we zoom in on the resonance of the 20 cm membrane and illustrate a day-long scan (gray region) made in intervals ${\tau }_{\mathrm{DM}}\approx 1.5\min$ with a step size equal to the detection bandwidth $\mathrm{\Delta }{\omega }_{\det }\approx 2\pi \times 0.2\mathrm{Hz}$.

Figure 3

Detector sensitivity near resonance, versus optical power, for the 10 cm membrane in Fig. 2, indicating sensitivity-bandwidth trade-offs due to thermal, backaction, and imprecision noise. Log-log (top) and log-linear (bottom) plots are shown for emphasis. The standard quantum limit (pink line) is achieved when backaction and imprecision noise are equal and can dominate thermal noise (dotted red line) off resonance. The width of ULDM signal is shaded blue.

Figure 4

Projected sensitivity to $B$-coupled dark photons. Blue curves are for centimeter-scale membranes as in Fig. 2, with the suppression factor $f_{12}$ adjusted for $B$ coupling. Black, red, and light blue curves are constraints set by the Eöt-Wash experiments, LIGO, and MICROSCOPE experiments, respectively.