  We study a method to cool down the vibration mode of a micro-mechanical beam
using a capacitively-coupled superconducting transmission line. The Coulomb
force between the transmission line and the beam is determined by the driving
microwave on the transmission line and the displacement of the beam. When the
frequency of the driving microwave is smaller than that of the transmission
line resonator, the Coulomb force can oppose the velocity of the beam. Thus,
the beam can be cooled. This mechanism, which may enable to prepare the beam in
its quantum ground state of vibration, is feasible under current experimental
conditions.
