Effective non-sinusoidal current phase dependence in d.c. SQUID’s

We show, by a first-order perturbative expansion with respect to the parameter \beta, that the dimensionality of the dynamical equations for the superconducting phase differences of a structurally symmetric conventional d.c. SQUID can be reduced from two to one. Taking completely into account the electromagnetic coupling of the two junctions, the resulting dynamical equation is seen to be similar to that of a single junction with an unconventional current-phase relation characterized by a second harmonic contribution. Effects of this unconventional term on the I-V characteristics of d.c. SQUID’s in the presence of an external rf field are presented