Coherent evolution and quantum transitions in a two level model of a SQUID ring

Using a quantum mechanical model for a frictionless superconducting quantum interference device ring subjected to a time varying external magnetic flux we solve the time-dependent Schrodinger equation for the ring and calculate the time-averaged energy and screening current expectation values. We demonstrate by computation that (subject to constraints on the applied field frequency and amplitude) the ring can be treated as a two level system. We also show that for certain regions of the bias flux, the time-averaged energy expectation value appears to jump between the time-averaged energies of the adiabatic ground and first excited states of the ring. (C) 1998 Academic Press.