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Multi-terminal superconducting Josephson junctions based on the proximityeffect offer the bright opportunity to tailor non trivial quantum states innanoscale weak-links. These structures can realize exotic topologies inmultidimensions as, for example, artificial topological superconductors able tosupport Majorana bound states, and pave the way to emerging quantumtechnologies and future quantum information schemes. Here, we report the firstrealization of a three-terminal Josephson interferometer based on a proximizednanosized weak-link. Our tunneling spectroscopy measurements reveal transitionsbetween gapped (i.e., insulating) and gapless (i.e., conducting) states, thosebeing controlled by the phase configuration of the three superconducting leadsconnected to the junction. We demonstrate the $topological$ nature of thesetransitions: a gapless state necessarily occurs between two gapped states ofdifferent topological index, very much like the interface between twoinsulators of different topology is necessarily conducting. The topologicalnumbers characterizing such gapped states are given by superconducting phasewindings over the two loops forming the Josephson interferometer. Since thesegapped states cannot be transformed to one another continuously withouthpassing through a gapless condition, these are topologically $protected$. Ourobservation of the gapless state is pivotal for enabling phase engineering ofmore sophisticated artificial topological materials realizing Weyl points orthe anomalous Josephson effect.

The $\omega$-SQUIPT: phase-engineering of Josephson topological materials