We demonstrate an accurate method to control the motion of a micromechanical oscillator in contact with a thermal bath. The experiment is carried out on the cantilever tip of an Atomic Force Microscope (AFM). Applying an appropriate time dependent external force, we decrease the time necessary to reach equilibrium by two orders of magnitude compared to the intrinsic equilibration time. Finally, we analyze the energetic cost of such a fast equilibration, by measuring with kBT accuracy the energy exchanges along the process.
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