  We study the ground states of low-density hadronic matter and high-density
color-flavor locked color superconducting phase in three-flavor QCD at finite
baryon chemical potential under rotation. We find that, in both cases under
sufficiently fast rotation, the combination of the rotation-induced topological
term for the eta' meson and the QCD anomaly leads to an inhomogeneous
condensate of the eta' meson, known as the chiral soliton lattice (CSL). We
find that, when baryon chemical potential is much larger than isospin chemical
potential, the critical angular velocity for the realization of the eta' CSL is
much smaller than that for the pi_0 CSL found previously. We also argue that
the eta' CSL states in flavor-symmetric QCD at low density and high density
should be continuously connected, extending the quark-hadron continuity
conjecture in the presence of the rotation.
