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 magneto-mechanical coupling between paramagnetic atoms and a current carrying, suspended nanowire. Atomic spin flips produce a back-action 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 find a non-trivial threshold detuning for the amplification and determine the threshold coupling.