Phonon Squeezing in a Superconducting Molecular Transistor
  Josephson transport through a single molecule or carbon nanotube is considered in the presence of a local vibrational mode coupled to the electronic charge. The ground-state solution is obtained exactly in the limit of a large superconducting gap, and is extended to the general case by variational analysis. Coherent charge fluctuations are entangled with non-classical phonon states. The Josephson current induces squeezing of the phonon mode, which is controlled by the superconducting phase difference and by the junction asymmetry. Optical probes of non-classical phonon states are briefly discussed. 
A. Zazunov (LEPES, CPT, PMMC), D. Feinberg (LEPES), Thierry Martin   (CPT)