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

We consider the possibility of parametric amplification of a mechanical vibration mode of a nanowire due to its interaction with a Bose-Einstein condensate (BEC) of ultracold atoms. The magneto-mechanical coupling is mediated by the vibrationally modulated magnetic field around the current-carrying nanowire, which can induce atomic transitions between different hyperfine sublevels. We theoretically analyze the limitations arising from the fact that the spin inverted atomic medium which feeds the mechanical oscillation has a finite bandwidth in the range of the chemical potential of the condensate.