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We present an experimental study on the non-equilibrium tunnel dynamics oftwo coupled one-dimensional Bose-Einstein quasi-condensates deep in theJosephson regime. Josephson oscillations are initiated by splitting a singleone-dimensional condensate and imprinting a relative phase between thesuperfluids. Regardless of the initial state and experimental parameters, thedynamics of the relative phase and atom number imbalance shows a relaxation toa phase-locked steady state. The latter is characterized by a high phasecoherence and reduced fluctuations with respect to the initial state. Wepropose an empirical model based on the analogy with the anharmonic oscillatorto describe the effect of various experimental parameters. A microscopic theorycompatible with our observations is still missing.

Relaxation to a Phase-locked Equilibrium State in a One-dimensional Bosonic Josephson Junction