  The Josephson effect is a prominent phenomenon of quantum supercurrents that
has been widely studied in superconductors and superfluids. Typical Josephson
junctions consist of two real-space superconductors (superfluids) coupled
through a weak tunneling barrier. Here we propose a momentum-space Josephson
junction in a spin-orbit coupled Bose-Einstein condensate, where states with
two diffferent momenta are coupled through Raman-assisted tunneling. We show
that Josephson currents can be induced not only by applying the equivalent of
"voltages", but also by tuning tunneling phases. Such tunneling-phase-driven
Josephson junctions in momentum space are characterized through both full mean
field analysis and a concise two-level model, demonstrating the important role
of interactions between atoms. Our scheme provides a platform for
experimentally realizing momentum-space Josephson junctions and exploring their
applications in quantum-mechanical circuits.
