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

Hybrid Josephson junctions (JJs) realized in superconductor-semiconductor heterostructures host fermionic modes known as Andreev bound states (ABSs). In JJs with three or more superconducting terminals, ABSs form synthetic band structures as a function of multiple superconducting phase differences which were predicted to exhibit novel properties, including lifting of the spin degeneracy, ground state parity transitions, and topological states. We present the realization of a phase-controlled InAs/Al three-terminal JJ and report on spectroscopic measurements of its ABS band structure. We find signatures of spin-degeneracy breaking, with level splitting in excess of ∼9  GHz, and zero-energy crossings associated to ground state fermion parity transitions. Spin splitting and parity transitions are enabled and controlled by locally applied magnetic fluxes, without the need for Zeeman effect or Coulomb blockade. Our results highlight the potential of multiterminal hybrid devices for phase engineering ABSs, with significant implications for spin- and parity-based quantum devices.