Generation of squeezing: magnetic dipoles on cantilevers*

We investigate the generation of motional squeezed states in a nano-mechanical cantilever. Our model system consists of a nanoscale cantilever -- whose center-of-mass motion is initially cooled to its quantum mechanical ground state -- magnetically coupled a classically driven mechanical tuning fork. We show that the magnetic dipole-dipole interaction can produce significant phonon squeezing of the center-of-mass motion of the cantilever, and evaluate the effect of various dissipation channels, including the coupling of the cantilever to a heat bath and phase and amplitude fluctuations in the oscillating field driving the tuning fork.