We consider the interaction of a quantum mechanical SQUID ring with aclassical resonator (a parallel $LC$ tank circuit). In our model we assume thatthe evolution of the ring maintains its quantum mechanical nature, even thoughthe circuit to which it is coupled is treated classically. We show that whenthe SQUID ring is driven by a classical monochromatic microwave source, energycan be transferred between this input and the tank circuit, even when thefrequency ratio between them is very large. Essentially, these calculationsdeal with the coupling between a single macroscopic quantum object (the SQUIDring) and a classical circuit measurement device where due account is taken ofthe non-perturbative behaviour of the ring and the concomitant non-linearinteraction of the ring with this device.
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