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. Schmiedmayer^1,2 Correspondence and requests for materials should be addressed to J.S. (Email: schmiedmayer@atomchip.org).

Abstract

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 weakly^{4, 5, 6, 7} and strongly^{8, 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 systems^{14, 15, 16}. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

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. Schmiedmayer^1,2 Correspondence and requests for materials should be addressed to J.S. (Email: schmiedmayer@atomchip.org).

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