  We study the non-equilibrium dynamics of a coherently split one-dimensional
(1d) Bose gas by measuring the full probability distribution functions of
matter-wave interference. Observing the system on different length scales
allows us to probe the dynamics of excitations on different energy scales,
revealing two distinct length-scale dependent regimes of relaxation. We measure
the crossover length-scale separating these two regimes and identify it with
the prethermalized phase-correlation length of the system. Our approach enables
a direct observation of the multimode dynamics characterizing one-dimensional
quantum systems.
