  We theoretically study cooling of flexural modes of a mechanical oscillator
by Bose-Einstein Condensate (BEC) atoms (Rb87) trapped in a magnetic trap. The
mechanical oscillator with a tiny magnet attached on one of its free ends
produces an oscillating magnetic field. When its oscillating frequency matches
certain hyperfine Zeeman energy of Rb87 atoms, the trapped BEC atoms are
coupled out of the magnetic trap by the mechanical oscillator, flying away from
the trap with stolen energy from the mechanical oscillator. Thus the mode
temperature of the mechanical oscillator is reduced. The mode temperature of
the steady state of a mechanical oscillator, measured by the mean steady-state
phonon number in the flexural mode of the mechanical oscillator, is analyzed.
It is found that ground state (phonon number less than 1) may be accessible
with optimal parameters of the hybrid system of a mechanical oscillator and
trapped BEC atoms.
