  Spin-orbit coupled ultra-cold atoms provide an intriguing new avenue for the
study of rich spin dynamics in superfluids. In this Letter, we observe
Zitterbewegung, the simultaneous velocity (thus position) and spin
oscillations, of neutral atoms between two spin-orbit coupled bands in a
Bose-Einstein condensate (BEC) through sudden quantum quenches of the
Hamiltonian. The observed Zitterbewegung oscillations are perfect on a short
time scale but gradually damp out on a long time scale, followed by sudden and
strong heating of the BEC. As an application, we also demonstrate how
Zitterbewegung oscillations can be exploited to populate the upper spin-orbit
band, and observe a subsequent dipole motion. Our experimental results are
corroborated by a theoretical and numerical analysis and showcase the great
flexibility that ultra-cold atoms provide for investigating rich spin dynamics
in superfluids.
