  The Landau-Zener (LZ) transition is one of the most fundamental phenomena in
quantum dynamics. It describes nonadiabatic transitions between quantum states
near an avoided crossing that can occur in diverse physical systems. Here we
report experimental measurements and tuning of LZ transitions between the
dressed eigenlevels of a Bose-Einstein condensate (BEC) that is synthetically
spin-orbit (SO) coupled. We measure the transition probability as the BEC is
accelerated through the SO avoided crossing and study its dependence on the
coupling between the diabatic (bare) states, eigenlevel slope, and eigenstate
velocity--the three parameters of the LZ model that are independently
controlled in our experiments. Furthermore, we performed time-resolved
measurements to demonstrate the breaking down of the spin-momentum locking of
the spin-orbit-coupled BEC in the nonadiabatic regime, and we determined the
diabatic switching time of the LZ transitions. Our observations show
quantitative agreement with the LZ model and numerical simulations of the
quantum dynamics in the quasimomentum space. The tunable LZ transition may be
exploited to enable a spin-dependent atomtronic transistor.
