Preparation and Detection of a Mechanical Resonator Near the Ground State of Motion

We have cooled the motion of a radio-frequency nanomechanical resonator by parametric coupling to a driven microwave frequency superconducting resonator. Starting from a thermal occupation of 480 quanta, we have observed occupation factors as low as 3.8$\pm$1.2 and expect the mechanical resonator to be found with probability 0.21 in the quantum ground state of motion. Cooling is limited by random excitation of the microwave resonator and heating of the dissipative mechanical bath.