Master's Defense: Elvira Caroline Jarmbæk Jacobsen

Properties of Multiterminal Josephson Junctions

The coupling of additional superconductors to the successful Josephson junction has been studied for decades. However, the experimental manifestation of the multiterminal Josephson effect was not accomplished before a few years ago. This motivates the theoretical studies of this thesis, which focuses on using a model describing the multiterminal Josephson junction by n equal superconductors coupled through a non-interacting single energy level of a quantum dot to cover a wide selection of properties. Based on this, we review and reproduce results of a range of previously found theoretical and experimental studies, both serving as a validation of the model and a springboard for adding new details.

The major topic concerns the conductance properties of a current-biased three-terminal Josephson junction. The impact of the Q factor is emphasised and it is shown how the regime of bias currents only slightly exceeding the critical current contour complicates the system dynamics, expressed through the behaviour of the multiplet resonances and the branches of reduced differential resistance. We study the deformation of the critical current contour in the presence of a magnetic field and find agreement with experimental results. Using a sinusoidal time-dependent magnetic field, half-integer Shapiro steps are demonstrated.

In addition, we propose a design for a protected superconducting qubit involving a three-terminal Josephson junction and suggest an accompanying gate method.