Axion dark matter search using arm cavity transmitted beams of
  gravitational wave detectors
  Axion is a promising candidate for ultralight dark matter which may cause a
polarization rotation of laser light. Recently, a new idea of probing the axion
dark matter by optical linear cavities used in the arms of gravitational wave
detectors has been proposed [Phys. Rev. Lett. 123, 111301 (2019)]. In this
article, a realistic scheme of the axion dark matter search with the arm cavity
transmission ports is revisited. Since photons detected by the transmission
ports travel in the cavity for odd-number of times, the effect of axion dark
matter on their phases is not cancelled out and the sensitivity at low-mass
range is significantly improved compared to the search using reflection ports.
We also take into account the stochastic nature of the axion field and the
availability of the two detection ports in the gravitational wave detectors.
The sensitivity to the axion-photon coupling, $g_{a\gamma}$, of the
ground-based gravitational wave detector, such as Advanced LIGO, with 1-year
observation is estimated to be $g_{a\gamma} \sim 3\times10^{-12}$ GeV$^{-1}$
below the axion mass of $10^{-15}$ eV, which improves upon the limit achieved
by the CERN Axion Solar Telescope.
