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-Pérot 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 \times 10 ^ { -13 } \text { ~ { } GeV } ^ { -1 } ( 4 \times 10 ^ { -14 } % \text { ~ { } GeV } ^ { -1 } ) at the axion mass m \simeq 3 \times 10 ^ { -13 } eV ( 2 \times 10 ^ { -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 \times 10 ^ { -17 } \text { ~ { % } 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 .