  Levitated optomechanical systems, and particularly particles trapped in
vacuum, provide unique platforms for studying the mechanical behavior of
objects well-isolated from their environment. Ultimately, such systems may
enable the study of fundamental questions in quantum mechanics, gravity, and
other weak forces. While the optical trapping of nanoparticles has emerged as
the prototypical levitated optomechanical system, it is not without problems
due to the heating from the high optical intensity required, particularly when
combined with a high vacuum environment. Here we investigate a
magneto-gravitational trap in ultra-high vacuum. In contrast to optical
trapping, we create an entirely passive trap for diamagnetic particles by
utilizing the magnetic field generated by permanent magnets and the
gravitational interaction. We demonstrate cooling the center of mass motion of
a trapped silica microsphere from ambient temperature to an effective
temperature near or below one milliKelvin in two degrees of freedom by optical
feedback damping.
