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

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.