Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions

We study a multi-terminal Josephson junction based on an interacting quantum dot coupled to $n$ superconducting BCS leads. Using an Anderson type model of a local level with an arbitrary onsite Coulomb repulsion, we uncover its surprising equivalence with an effective two-terminal junction with symmetric couplings to appropriately phase-biased leads. Regardless of the strength of the Coulomb interaction, this hidden symmetry enables us to apply well-established numerical and theoretical tools for exact evaluation of various physical quantities, and imposes strict relations among them. Focusing on three-terminal devices, we then demonstrate several phenomena such as the existence of the finite energy band crossings, superconducting transistor and diode effects, as well as current phase relation modulation.