  Thermal noise of a mirror is one of the most important issues in high
precision measurements such as gravitational-wave detection or cold damping
experiments. It has been pointed out that thermal noise of a mirror with
multi-layer coatings can be reduced by mechanical separation of the layers. In
this paper, we introduce a way to further reduce thermal noise by locking the
mechanically separated mirrors. The reduction is limited by the standard
quantum limit of control noise, but it can be overcome with a
quantum-non-demolition technique, which finally raises a possibility of
complete elimination of coating thermal noise.
