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 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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References
Popov, V. N. Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983)
Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, Oxford, 2003)
Haldane, F. Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids. Phys. Rev. Lett. 47, 1840–1843 (1981)
Petrov, D. S., Shlyapnikov, G. V. & Walraven, J. T. M. Regimes of quantum degeneracy in trapped 1D gases. Phys. Rev. Lett. 85, 3745–3749 (2000)
Dettmer, S. et al. Observation of phase fluctuations in elongated Bose-Einstein condensates. Phys. Rev. Lett. 87, 160406 (2001)
Richard, S. et al. Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates. Phys. Rev. Lett. 91, 010405 (2003)
Pricoupenko, L., Perrin, H. & Olshanii, M. Quantum Gases in Low Dimensions (Journal de Physique IV Proceedings, Vol. 116, EDP Sciences, 2004)
Paredes, B. et al. Tonks-Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004)
Kinoshita, T., Wenger, T. & Weiss, D. S. Observation of a one-dimensional Tonks-Girardeau gas. Science 305, 1125–1128 (2004)
Kinoshita, T., Wenger, T. R. & Weiss, D. S. A quantum Newton’s cradle. Nature 440, 900–903 (2006)
Schumm, T. et al. Matter wave interferometry in a double well on an atom chip. Nature Phys. 1, 57–62 (2005)
Burkov, A. A., Lukin, M. D. & Demler, E. Decoherence dynamics in low-dimensional cold atoms interferometers. Phys. Rev. Lett. 98, 200404 (2007)
Whitlock, N. K. & Bouchoule, I. Relative phase fluctuations of two coupled one-dimensional condensates. Phys. Rev. A 68, 053609 (2003)
Blatter, G., Feigelman, M., Geshkenbein, V., Larkin, A. & Vinokur, V. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994)
Shimshoni, E., Auerbach, A. & Kapitulnik, A. Transport through quantum melts. Phys. Rev. Lett. 80, 3352–3355 (1998)
Forte, S. Quantum mechanics and field theory with fractional spin and statistics. Rev. Mod. Phys. 64, 193–236 (1992)
Folman, R., Krüger, P., Schmiedmayer, J., Denschlag, J. & Henkel, C. Microscopic atom optics: From wires to an atom chip. Adv. At. Mol. Opt. Phys. 48, 263–356 (2002)
Fortagh, J. & Zimmermann, C. Magnetic microtraps for ultracold atoms. Rev. Mod. Phys. 79, 235 (2007)
Bouchoule, I., Kheruntsyan, K. V. & Shlyapnikov, G. V. Interaction-induced crossover versus finite-size condensation in a weakly interacting trapped one-dimensional Bose gas. Phys. Rev. A 75, 031606(R) (2007)
Hofferberth, S., Lesanovsky, I., Fischer, B., Verdu, J. & Schmiedmayer, J. Radio-frequency dressed state potentials for neutral atoms. Nature Phys. 2, 710–716 (2006)
Jo, G. B. et al. Matter-wave interferometry with phase fluctuating Bose-Einstein condensates. Preprint at 〈http://arxiv.org/abs/0706.4041v3〉 (2007)
Spietz, L., Lehnert, K. W., Siddiqi, I. & Schoelkopf, R. J. Primary electronic thermometry using the shot noise of a tunnel junction. Science 300, 1929–1932 (2003)
Gati, R., Hemmerling, B., Fölling, J., Albiez, M. & Oberthaler, M. K. Noise thermometry with two weakly coupled Bose-Einstein condensates. Phys. Rev. Lett. 96, 130404 (2006)
Bistritzer, R. & Altman, E. Intrinsic dephasing in one dimensional ultracold atom interferometers. Proc. Natl Acad. Sci. USA 104, 9955–9959 (2007)
Andreev, A. F. The hydrodynamics of two-dimensional and one-dimensional fluids. Sov. Phys. JETP 51, 1038–1040 (1980)
Rigol, M., Dunjko, V., Yurovsky, V. & Olshanii, M. Relaxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons. Phys. Rev. Lett. 98, 050405 (2007)
Cazalilla, M. Bosonizing one-dimensional cold atomic gases. J. Phys. B 37, S1–S47 (2004)
Ananikian, D. & Bergeman, T. The Gross-Pitaevskii equation for Bose particles in a double well potential: Two mode models and beyond. Phys. Rev. A 73, 013604 (2006)
Bouchoule, I. Modulational instabilities in Josephson oscillations of elongated coupled condensates. Eur. Phys. J. D 35, 147–154 (2005)
Gritsev, V., Polkovnikov, A. & Demler, E. Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms. Phys. Rev. B 75, 174511 (2007)
Gritsev, V., Demler, E., Lukin, M. & Polkovnikov, A. Analysis of quench dynamics of coupled one dimensional condensates using quantum sine Gordon model. Preprint at 〈http://arxiv.org/cond-mat/0702343〉
Wildermuth, S. et al. Optimized magneto-optical trap for experiments with ultracold atoms near surfaces. Phys. Rev. A 69, 030901 (2004)
Groth, S. et al. Atom chips: Fabrication and thermal properties. Appl. Phys. Lett. 85, 2980–2982 (2004)
Krüger, P. et al. Disorder potentials near lithographically fabricated atom chips. Preprint at 〈http://arxiv.org/cond-mat/0504686〉 (2004)
Wildermuth, S. et al. Sensing electric and magnetic fields with Bose-Einstein condensates. Appl. Phys. Lett. 88, 264103 (2006)
Lesanovsky, I. et al. Adiabatic radio frequency potentials for the coherent manipulation of matter waves. Phys. Rev. A 73, 033619 (2006)
Hofferberth, S., Fischer, B., Schumm, T., Schmiedmayer, J. & Lesanovsky, I. Ultracold atoms in radio-frequency dressed potentials beyond the rotating-wave approximation. Phys. Rev. A 76, 013401 (2007)
Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006)
Gerbier, F. Quasi-1d Bose-Einstein condensates in the dimensional crossover regime. Europhys. Lett. 66, 771–777 (2004)
Smerzi, A., Fantoni, S., Giovanazzi, S. & Shenoy, S. R. Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates. Phys. Rev. Lett. 79, 4950–4953 (1997)
Röhrl, A., Naraschewski, M., Schenzle, A. & Wallis, H. Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment. Phys. Rev. Lett. 78, 4143–4146 (1997)
Fisher, N. I. Statistical Analysis of Circular Data (Cambridge Univ. Press, Cambridge, UK, 1993)
Acknowledgements
We thank A Burkov, V. Gritsev, E. Demler, R. Bistritzer and E. Altman for discussions. We also thank S. Groth for fabricating the atom chip used in the experiments. We acknowledge financial support from the Wittgenstein Prize and the European Union, through Atom Chips and FET/QIPC SCALA projects.
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Hofferberth, S., Lesanovsky, I., Fischer, B. et al. Non-equilibrium coherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007). https://doi.org/10.1038/nature06149
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DOI: https://doi.org/10.1038/nature06149
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