Non-equilibrium coherence dynamics in one-dimensional Bose gases

Low-dimensional systems provide beautiful examples of many-body quantum physics(1). For one-dimensional (1D) systems(2), the Luttinger liquid approach(3) provides insight into universal properties. Much is known of the equilibrium state, both in the weakly(4-7) and strongly(8,9) interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached(10). Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state(11). The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions(12). For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach(13). This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems(14-16). Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.