Theory of superconducting π-qubit with a ferromagnetic insulator

A strong exchange field acting on the electrons in a ferromagnet-metal (FM) provokes the damped oscillatory behavior of the superconducting order parameter. This effect is an origin of the π-junction realization in superconductor-FM-superconductor (S-FM-S) systems. In the π-junction SQUID, a quantum coherent two-level state (qubit) is formed without an external magnetic field. Therefore, it is believed that this system becomes a quiet qubit. In the S-FM-S systems, however, the quasiparticle excitation in FM region gives rise to a strong Ohmic dissipation, so that the coherence time becomes very short. Instead, we theoretically propose a new π-junction qubit which consists of a superconducting ring with a ferromagnetic insulator (FI). We show that the quasiparticle dissipation of this S-FI-S ring (SQUID) is very weak. This feature and the quietness of this system make it possible to realize a qubit with long decoherence time.