Letter

Nature 449, 324-327 (20 September 2007) | doi:10.1038/nature06149; Received 14 June 2007; Accepted 2 August 2007

Non-equilibrium coherence dynamics in one-dimensional Bose gases

S. Hofferberth1,2, I. Lesanovsky3, B. Fischer1, T. Schumm2 & J. Schmiedmayer1,2

  1. Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany
  2. Atominstitut der Österreichischen Universitäten, TU-Wien, Stadionallee 2, A-1020 Vienna, Austria
  3. Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria

Correspondence to: J. Schmiedmayer1,2 Correspondence and requests for materials should be addressed to J.S. (Email: schmiedmayer@atomchip.org).

Low-dimensional systems provide beautiful examples of many-body quantum physics1. For one-dimensional (1D) systems2, the Luttinger liquid approach3 provides insight into universal properties. Much is known of the equilibrium state, both in the weakly4, 5, 6, 7 and strongly8, 9 interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached10. 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 state11. 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 predictions12. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach13. 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 systems14, 15, 16. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

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