Instabilities in Arrays of Coupled SQUIDs

Previous work on chains of RF SQUIDs has exposed repeatable hysteretic jumps in the frequency modulation curve. In this thesis we show that this may be explained by a nearest neighbour interaction between the SQUIDs in the chain. Further modelling shows that these jumps arise from hysteresis in the flux configuration of the array. This hysteresis may be present even for β_L < 1. We find that the behaviour of each SQUID is dependent on its position within the array even for an array of identical SQUIDs. Studies of the behaviour of different length arrays shows qualitatively different behaviour for different array lengths. We explore the sensitivity of the array to deviation in SQUID parameters such as loop area and critical current in different coupling regimes. We show that the effect of the coupling may be alleviated by the increasing the loop inductance of the SQUIDs away from the array edge. Subsequently, we present the results of an experiment designed to provide clearer data in order to understand the effect of the coupling. The sample consisted of a short nanoSQUID array in a resonator. Comparisons to the theory show some agreement, although the nanoSQUIDs exhibited a high degree of hysteresis in the current phase relation at both milliKelvin temperatures and temperatures approaching T_c.