SQUID Detection of Quantized Mechanical Motion

We predict that quantized mechanical motion can be detected by embedding a mechanical resonator into a quantum SQUID. If the system is tuned to the regime when a plasma frequency of the SQUID matches the resonator frequency, the doubly-degenerate quantum level of the system is split by the coupling between the SQUID and the resonator. Observation of an avoided crossing as the function of external flux would be an unambiguous evidence of quantum nature of mechanical motion. We also investigate the conditions maximizing the level splitting.