Josephson junctions represent a mature class of quantum devices that serve as ultra-sensitive sensors and are envisaged as fundamental building blocks for future quantum computers. They typically consist of two superconducting leads and a central scattering region. We extend this paradigm by connecting multiple leads to a centrally placed quantum dot, which provides enhanced control over the device's electrical and magnetic properties. The increasing complexity makes such systems notoriously difficult to mathematically analyze. We avoid these problems by discovering a novel geometric symmetry that allows us to fully solve and understand the complicated physics by performing calculations on a simpler two-lead system with symmetric couplings and an appropriate phase bias. We characterize this mapping completely through a single geometric factor χ that captures all the intricate multilead physics in one elegant parameter.
Our discovery allows researchers to use well-established computational tools to perform previously impossible calculations for these complex quantum devices. Focusing on three-lead systems, we demonstrate various funcionalities including superconducting transistors and diodes, as well as the ability to control current flow through phase manipulation. Our breakthrough provides both fundamental understanding of how these quantum systems work and practical methods to study novel classes of multilead quantum devices. This geometric approach opens pathways for tackling even more advanced device architectures with enhanced capabilities.
(a) Four quantum dots are arranged in series and attached to ten superconducting terminals (green color). Geometric factors χ1, χ2 and χ4 fully characterize the geometric symmetries of the corresponding dots, enabling an effective system mapping as indicated. (b) Three quantum dots forming a cyclic configuration with twelve superconducting leads. (c) The top panel shows χi. Subsequently, in the bottom panel, a rotation by −δi and a decomposition into two complex conjugated vectors of length 1/2 is performed. After rotating back, it is shown that χi can be mapped onto its counterpart with just two leads symmetrically coupled to the dot. (d) Example of a system for which the method cannot be applied: parallel double quantum dot/level system attached to two superconducting leads.