  We propose a scheme in which the quantum coherence of a nanomechanical
resonator can be probed using a superconducting qubit. We consider a mechanical
resonator coupled capacitively to a Cooper-pair box and assume that the
superconducting qubit is tuned to the degeneracy point so that its coherence
time is maximised and the electro-mechanical coupling can be approximated by a
dispersive Hamiltonian. When the qubit is prepared in a superposition of states
this drives the mechanical resonator progressively into a superposition which
in turn leads to apparent decoherence of the qubit. Applying a suitable control
pulse to the qubit allows its population to be inverted resulting in a reversal
of the resonator dynamics. However, the resonator's interactions with its
environment mean that the dynamics is not completely reversible. We show that
this irreversibility is largely due to the decoherence of the mechanical
resonator and can be inferred from appropriate measurements on the qubit alone.
Using estimates for the parameters involved based on a specific realization of
the system we show that it should be possible to carry out this scheme with
existing device technology.
