The effect of the resonant mode structure on flux tunneling in SQUIDs

The problem of macroscopic quantum tunneling in SQUIDs is discussed, taking into account the resonant mode structure of typical devices. These are evaluated for the particular case of a SQUID formed from a conical point intersecting a hemispherical cavity, and it is shown that the conventional representation of a SQUID as a Josephson junction in parallel with an inductor and a capacitor is a good first approximation in most cases, provided the inductance and capacitance used are those of the whole device rather than of the weak link alone. The discussion is extended to another case of practical importance, where such a cavity is connected to an outer hole by a flange, and it is found that if the capacitance of the flange is large, the tunneling behavior is largely independent of the presence of the outer hole, apart from the effects of any dc bias.