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

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