Coupling of electronic and vibrational degrees of freedom in systems with superconducting leads further enriches the physics in tunneling systems. We consider back-action effects of the current on the mechanical motion of a subsystem and show that the mechanical oscillations can be externally excited by the supercurrent. On the other hand, the nanomechanical motion leaves off-prints in the supercurrent which may lead to e.g. additional Shapiro steps in the I–V characteristics. We finally investigate the dynamics of a vibrating quantum dot embedded in a Josephson junction, and we find that new time-scales emerge. These emergent time-scales are intimately related to the energies of the single-electron transitions occurring in the quantum dot. We derive a phase diagram for the dynamics of the quantum dot occupation. In particular, we find one regime in which the occupation numbers are constants of the motion and in which the mechanical dynamics is, thus, set by the Josephson frequency.
KeywordsBias Voltage Josephson Junction Occupation Number Mechanical Motion Tunneling Rate