  Establishment of phase-coherence and a non-dissipative (super)current between
two weakly coupled superconductors, known as the Josephson effect, plays a
foundational role in basic physics and applications to metrology, precision
sensing, high-speed digital electronics, and quantum computing. The junction
ranges from planar insulating oxides to single atoms, molecules, semiconductor
nanowires, and generally to any finite-size coherent conductor. Recently,
junctions of more than two superconducting terminals gained broad attention in
the context of braiding of Majorana fermions in the solid state for
fault-tolerant quantum computing, and accessing physics and topology in
dimensions higher than three. Here we report the first observation of Josephson
effect in 3- and 4-terminal junctions, fabricated in a top-down fashion from a
semiconductor/superconductor (InAs/Al) epitaxial two-dimensional
heterostructure. Due to interactions, the critical current of an N-terminal
junction becomes the boundary of an (N-1)-dimensional manifold of
simultaneously allowed supercurrents. The measured shapes of such manifolds are
explained by the scattering theory of mesoscopic superconductivity, and they
can be remarkably sensitive to the junction's symmetry class. Furthermore, we
observed a notably high-order (up to 8) multiple Andreev reflections
simultaneously across every terminals pair, which verifies the multi-terminal
nature of normal scattering and a high interface quality in our devices. Given
the previously shown gate-control of carrier density and evidence of spin-orbit
scattering in InAs/Al heterostructures, and device compatibility with other 2D
materials, the multi-terminal Josephson effect reported here can become a
testbed for physics and applications of topological superconductivity.
