  We propose a possibility of a phonon laser by coupling a Bose-Einstein
condensate to a nanomechanical cantilever with a magnetic tip. Due to the
magnetic coupling, atomic spin flips induce cantilever motion which can be used
to produce a phonon laser. The system is described by the equivalent of the
Jaynes-Cummings Hamiltonian. By controlling the number of atoms and the
population inversion, one can obtain either a continuous wave (cw) or transient
lasing. The two-body atom-atom interaction is also shown to coherently
manipulate the lasing process. We also show that in the strong coupling limit,
the same system can undergo a Dicke-Hepp-Lieb superradiant phase transition.
Exotic phase diagrams can be obtained by tuning the two body atom-atom
interaction.
