We investigate the nonstationary boundary effect for a quantum flux in a double rf-SQUID system. In a superconducting ring interrupted by a dc-SQUID (so-called double rf-SQUID), the Josephson potential can be controlled by the magnetic flux through the dc-SQUID ring. This system is equivalent to an anharmonic oscillator with a time-dependent frequency. A rapid change of the magnetic flux in the dc-SQUID leads to the nonadiabatic mixing of the quantum states for a quantum flux in a double rf-SQUID. Therefore, this becomes a circuit analogue of the dynamical Casimir effect in quantum field theory. We perform numerical calculations for the quantum state evolution of the quantum flux within a harmonic approximation, taking account of the nonadiabatic effect. We found that the resulting state distribution has a super-Poissonian character that reflects flux squeezing caused by the Bogoliubov transformation between eigenstates at different times.
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