A Study of Josephson Junction Characteristics.

Abstract: This Bachelor thesis has as its aim to investigate Josephson junctions by examining their I-V characteristics and to visualize various phenomena associated with Josephson junctions. Primarily, everything considered in this thesis uses a semi-classical model where quantum eects have been excluded. The thesis focuses on 1D arrays of Josephson junctions fed with direct current with the goal to study what occurs when many junctions are placed in a row. First a single Josephson junction is simulated and we observe a hysteresis in the I-V characteristics that is examined. Secondly a 1-D array is considered and the coupled system of dierential equations that follows is solved numerically, and from this data the properties of Josephson junctions are deduced. We discovered that this array generally has similar properties to a single Josephson junction. We also sought to replicate results obtained experimentally in the lab by David Haviland and his co-workers at KTH, but by simulations, to see how good our models are. We have produced data agreeing partly with the experimental results and we have had no directly contradicting outcomes from our simulations. An explicit relation between the number of Josephson junctions and the feature of the I-V characteristics was derived and the validity of our model was strengthened by the consistency of our results.