We consider the interaction of a quantum mechanical SQUID ring with a
classical resonator (a parallel LC tank circuit). In our model we assume that
the evolution of the ring maintains its quantum mechanical nature, even though
the circuit to which it is coupled is treated classically. We show that when
the SQUID ring is driven by a classical monochromatic microwave source, energy
can be transferred between this input and the tank circuit, even when the
frequency ratio between them is very large. Essentially, these calculations
deal with the coupling between a single macroscopic quantum object (the SQUID
ring) and a classical circuit measurement device where due account is taken of
the non-perturbative behaviour of the ring and the concomitant non-linear
interaction of the ring with this device.Comment: 7 pages, 6 figure
