  Axion dark matter differentiates the phase velocities of the
circular-polarized photons. In Phys.Rev.Lett. 123 (2019) no.11, 111301, we have
proposed a scheme to measure the phase difference by using a linear optical
cavity. 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
$g_{\text{a}\gamma} \simeq 8\times10^{-13} \text{GeV}^{-1}\, (4 \times
10^{-14}\text{GeV}^{-1})$ at the axion mass $m \simeq 3\times 10^{-13}$ 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
$g_{\text{a}\gamma} \simeq 10^{-14} \text{GeV}^{-1}\ (8\times10^{-17}
\text{GeV}^{-1})$ at $m = 1.563\times10^{-10}$ eV ($1.563\times10^{-11}$ eV).
This sensitivity can be achieved without loosing any sensitivity to
gravitational waves.
