  We report on the observation of the phase dynamics of interacting
one-dimensional ultracold bosonic gases with two internal degrees of freedom.
By controlling the non-linear atomic interactions close to a Feshbach resonance
we are able to induce a phase diffusive many-body spin dynamics. We monitor
this dynamical evolution by Ramsey interferometry, supplemented by a novel,
many-body echo technique. We find that the time evolution of the system is well
described by a Luttinger liquid initially prepared in a multimode squeezed
state. Our approach allows us to probe the non-equilibrium evolution of
one-dimensional many-body quantum systems.
