Coherent states in a multi-junction superconducting loop

The mutual coherent interaction of Josephson junctions in a multi-junction superconducting loop (MSL) in the limit of zero-loop inductance is theoretically investigated. For the loop containing 2 M junctions there are M coherent states corresponding to different values of effective flux ϕ eff in the loop. The stability analysis using the method of Floquet exponents shows the highest stability for the state with ϕ eff = 1/2. In this state, the MSL behaves like an oscillating magnetic dipole. The optimum stability is reached for the normalised bias current i b ≃ 2.5 and the McCumber parameter β C ≃ 0.5.