  The momentum space Josephson effect describes the supercurrent flow between
weakly coupled Bose-Einstein condensates (BECs) at two discrete momentum
states. Here, we experimentally observe this exotic phenomenon using a BEC with
Raman-induced spin-orbit coupling, where the tunneling between two local band
minima is implemented by the momentum kick of an additional optical lattice. A
sudden quench of the Raman detuning induces coherent spin-momentum oscillations
of the BEC, which is analogous to the a.c. Josephson effect. We observe both
plasma and regular Josephson oscillations in different parameter regimes. The
experimental results agree well with the theoretical model and numerical
simulation, and showcase the important role of nonlinear interactions. We also
show that the measurement of the Josephson plasma frequency gives the
Bogoliubov zero quasimomentum gap, which determines the mass of the
corresponding pseudo-Goldstone mode, a long-sought phenomenon in particle
physics. The observation of momentum space Josephson physics offers an exciting
platform for quantum simulation and sensing utilizing momentum states as a
synthetic degree.
