Axion Dark Matter Search with Interferometric Gravitational Wave Detectors

Axion dark matter differentiates the phase velocities of the circular-polarized photons. In this Letter, a scheme to measure the phase difference by using a linear optical cavity is proposed. If the scheme is applied to the Fabry-P'erot arm of Advanced LIGO-like (Cosmic-Explorer-like) gravitational wave detector, the potential sensitivity to the axion-photon coupling constant, $g_{\text{a}\gamma }$, reaches $g_{$\text{a}$\gamma} \simeq 8\times10^{-13}$GeV$^{-1}, (4 \times 10^{-14}$GeV$^{-1})$attheaxionmass$m \simeq 3\times 10^{-13}$eV($2\times10^{-15}$ eV) and remains at around this sensitivity for 3 orders of magnitude in mass. Furthermore, its sensitivity has a sharp peak reaching $g_{\text{a}\gamma }\simeq {10}^{-14}$ GeV${}^{-1}$ $(8\times {10}^{-17}$ GeV${}^{-1})$ at $m=1.563\times {10}^{-10}$ eV ($1.563\times {10}^{-11}$ eV). This sensitivity can be achieved without loosing any sensitivity to gravitational waves.