Parametric amplification of the mechanical vibrations of a suspended nanowire by magnetic coupling to a Bose-Einstein condensate

We show how the vibrational modes of a nanowire may be coherently manipulated with a Bose-Einstein condensate of ultracold atoms. We consider the magnetomechanical coupling between paramagnetic atoms and a suspended nanowire carrying a dc current. Atomic spin flips produce a backaction onto the wire vibrations, which can lead to mechanical mode amplification. In contrast to systems considered before, the condensate has a finite energy bandwidth in the range of the chemical potential and we explore the consequences of this on the parametric drive. Applying the resolvent method, we determine the threshold coupling and we also find a significant frequency shift of the vibration due to magnetomechanical dressing.