  We report the levitation of a superconducting lead-tin sphere with 100
micrometer diameter (corresponding to a mass of 5.6 micrograms) in a static
magnetic trap formed by two coils in an anti-Helmholtz configuration, with
adjustable resonance frequencies up to 240 hertz. The center-of-mass motion of
the sphere is monitored magnetically using a dc superconducting quantum
interference device as well as optically and exhibits quality factors of up to
2.6e7. We also demonstrate 3D magnetic feedback control of the sphere's motion.
The setup is housed in a dilution refrigerator operating at 15 millikelvin. By
implementing a cryogenic vibration isolation system we can attenuate
environmental vibrations at 200 hertz by approximately seven orders of
magnitude. The combination of low temperature, large mass and high quality
factor as well as adjustable resonance frequencies provides a promising
platform for testing quantum physics in previously unexplored regimes with high
mass and long coherence times.
