The interpretation of experimentally measured magnetic susceptibilities of a SQUID ring in terms of the quantum mechanics of a double Josephson junction

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Abstract
For some years, experimental measurements of magnetic susceptibilities of SQUIDs have been reported and interpreted in terms of a quantum mechanical model that depends on the system having a very small capacitance ( F) and occupying different quantum energy states for macroscopically long times. This interpretation is criticized on the grounds that the relevant capacitance is very much larger and that the very long lifetimes are difficult to understand. An alternative model, consisting of a grain or island connected to the SQUID ring by two Josephson junctions, is proposed. The capacitance relevant to symmetric motion of charge on and off the island through the two junctions is then of the right order and the other degrees of freedom of the system are treated classically. The resulting susceptibilities are in reasonably good agreement with experiment. The question of the long lifetimes of the states is considered in some detail, and their implications for the conventional and normal-electron tunnelling resistance are analysed.