Phonon Squeezing in a Superconducting Molecular Transistor
Résumé
Josephson transport through a double junction formed by a single molecule or carbon nanotube is considered in the presence of a local vibrational mode which is linearly coupled to the charge on the molecule. An exact solution is obtained in the limit of a large superconducting gap, and it is complemented by a variational analysis in the general case. Coherent charge fluctuations involve polaron dressing and are entangled with non-classical phonon states. The flow of a Josephson current induces squeezing of the phonon mode, controlled by the superconducting phase difference and by the junction asymmetry. Squeezing is maximal in the polaron crossover regime, where a nearly minimum-uncertainty state with about 40 per cent squeezing can be obtained. Optical probes of non-classical states are briefly discussed.