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

Multimode dynamics and emergence of a characteristic length-scale in a one-dimensional quantum system