Spin-degeneracy breaking and parity transitions in three-terminal Josephson junctions

Harnessing spin and parity degrees of freedom is of fundamental importance for the realization of emergent quantum devices. Nanostructures embedded in superconductor--semiconductor hybrid materials offer novel and yet unexplored routes for addressing and manipulating fermionic modes. Here we spectroscopically probe the two-dimensional band structure of Andreev bound states in a phase-controlled hybrid three-terminal Josephson junction. Andreev bands reveal spin-degeneracy breaking, with level splitting in excess of 9 GHz, and zero-energy crossings associated to ground state fermion parity transitions, in agreement with theoretical predictions. Both effects occur without the need of external magnetic fields or sizable charging energies and are tuned locally by controlling superconducting phase differences. Our results highlight the potential of multiterminal hybrid devices for engineering quantum states.