Optomechanical platform for high-frequency gravitational wave and vector dark matter detection

TL;DR

This work proposes a unified optomechanical detector for high‑frequency gravitational waves and vector dark matter using a network of optically trapped silicon membranes near GaAs mirrors inside long optical cavities. Gravitational waves resonantly drive membrane motion via cavity length modulation, while vector dark matter couples through a B‑L–dependent differential acceleration between the membrane and mirror; optical spring tuning extends coverage from 0.5 to 40 kHz using six membranes. The design achieves a peak GW strain sensitivity of $h_{ m min} \approx 2\times 10^{-23}/\sqrt{\mathrm{Hz}}$ at 40 kHz and, for vector dark matter, probes the range $m_{\rm DM}\sim 2\times10^{-12}$–$2\times10^{-10}$ eV/$c^2$ over a one‑year measurement, surpassing Eöt‑Wash and LIGO/Virgo limits in this band. Overall, the platform offers a practical, scalable path to exploring high‑frequency gravitational physics and ultralight dark sectors in a single experimental approach.

Abstract

We present a proposal for a nanomechanical membrane resonator integrated into a moderate-finesse ($\mathcal{F}\sim 10$) optical cavity as a versatile platform for detecting high-frequency gravitational waves and vector dark matter. Gravitational-wave sensitivity arises from cavity-length modulation, which resonantly drives membrane motion via the radiation-pressure force. This force also enables in situ tuning of the membrane's resonance frequency by nearly a factor of two, allowing a frequency coverage from 0.5 to 40 kHz using six membranes. The detector achieves a peak strain sensitivity of $2\times 10^{-23}/\sqrt{\text{Hz}}$ at 40 kHz. Using a silicon membrane positioned near a gallium-arsenide input mirror additionally provides sensitivity to vector dark matter via differential acceleration from their differing atomic-to-mass number ratios. The projected reach surpasses the existing limits in the range of $2\times 10^{-12}$ to $2\times 10^{-10}$ $\text{eV}/c^2$ for a one-year measurement. Consequently, the proposed detector offers a unified approach to searching for physics beyond the Standard Model, probing both high-frequency gravitational waves and vector dark matter.

Figures (3)

• Figure 1: Schematic of the optomechanical detector platform. (a) A nanomechanical silicon (Si) membrane (gray) is positioned near the gallium arsenide (GaAs) input mirror inside an optical cavity of length $L$. The membrane’s equilibrium position coincides with an antinode of an optical trapping field (red) with power $\mathcal{P}_\mathrm{trap}$, which tunes the membrane’s resonance frequency $\Omega_\mathrm{eff}(\mathcal{P}_\mathrm{trap})/2\pi$. A passing gravitational wave at this frequency resonantly excites the membrane to oscillate with amplitude $x$, which is measured via a probe field (blue). The combination of the GaAs input mirror and Si membrane allows simultaneous sensitivity to vector dark matter models, due to both materials' distinct baryon and lepton number. Only one optomechanical cavity is shown; the full detector uses two in a Michelson configuration to suppress technical noise. (b) The mode shapes of the first and second symmetric modes, denoted s1 (upper) and s2 (lower) respectively, simulated with COMSOL Multiphysics COMSOL, of an ultra-high-$Q$ trampoline membrane featuring branched tethers.
• Figure 2: a) Strain sensitivity to high frequency gravitational waves. Darker traces correspond to the s1 mode while lighter traces represent the s2 mode (see Fig. \ref{['fig:general']}(b)). Blue traces represent the best case sensitivity at every resonant frequency. Red traces are six specific membrane designs, where the resonant frequency is tuned by increasing the optical trapping power from 1 to 20W. s2 modes are shown only for the three membrane designs with the highest resonance frequencies. The aLIGO design sensitivity is shown in grey LIGOGWLimits. b) Damping rates contributing to Eq. \ref{['eq:gamma']}, as well as the effective mass, for the best case scenario. Discontinuities are due to the designs yielding the best sensitivity switching from being a sweep of the lateral extent at the maximum pad size and stress to a sweep of the pad size at the maximum lateral extent and stress. c) Same as b) but for the six specific tuned membrane designs.
• Figure 3: Shows the sensitivity at the membrane's resonance frequency to different $B-L$ coupled and $B$ coupled dark matter masses of the best-case scenario membranes (blue) and the same six optically-tuned membrane designs as in Figure \ref{['fig:sensitivity']}a (red). The dotted lines correspond to a measurement time of $\tau=\tau_{DM}$ while solid lines correspond to $\tau=$1 year. Darker lines represent the s1 mode, while lighter lines correspond to the s2 mode [see Fig. \ref{['fig:general']}]. Existing limits are shown AxionLimits, which are from aLIGO and Virgo VDMLimitsLIGO and the Eöt-Wash experiment VDMLimitsEotWash.