Ultralight vector dark matter search with auxiliary length channels of
  gravitational wave detectors
  Recently, a considerable amount of attention has been given to the search for
ultralight dark matter by measuring the oscillating length changes in the arm
cavities of gravitational wave detectors. Although gravitational wave detectors
are extremely sensitive for measuring the differential arm length changes, the
sensitivity to dark matter is largely attenuated, as the effect of dark matter
is mostly common to arm cavity test masses. Here, we propose to use auxiliary
length channels, which measure the changes in the power and signal recycling
cavity lengths and the differential Michelson interferometer length. The
sensitivity to dark matter can be enhanced by exploiting the fact that
auxiliary interferometers are more asymmetric than two arm cavities. We show
that the sensitivity to $U(1)_{B-L}$ gauge boson dark matter with masses below
$7\times 10^{-14}$ eV can be greatly enhanced when our method is applied to a
cryogenic gravitational wave detector KAGRA, which employs sapphire test masses
and fused silica auxiliary mirrors. We show that KAGRA can probe more than an
order of magnitude of unexplored parameter space at masses around $1.5 \times
10^{-14}$ eV, without any modifications to the existing interferometer.
