Decoherence and recoherence in a vibrating rf SQUID

We study an rf SQUID, in which a section of the loop is a freely suspended beam that is allowed to oscillate mechanically. The coupling between the rf SQUID and the mechanical resonator originates from the dependence of the total magnetic flux threading the loop on the displacement of the resonator. Motion of the latter affects the visibility of Rabi oscillations between the two lowest energy states of the rf SQUID. We address the feasibility of experimental observation of decoherence and recoherence, namely decay and rise of the visibility, in such a system.