  We present a microscopic calculation of the nondissipative current through a
superconducting quantum point contact coupled to a mechanical oscillator. Using
the non-equilibrium Keldysh Green function approach, we determine the
current-phase relation. The latter shows that at certain phases, the current is
sharply suppressed. These dips in the current-phase relation provide
information about the oscillating frequency and coupling strength of the
mechanical oscillator. We also present an effective two-level model from which
we obtain analytical expressions describing the position and width of the dips.
Our findings are of relevance for nanomechanical resonators based on
superconducting materials.
