It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable1,2. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space3. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue4,5,6, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.
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Coleman, S. Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D 11, 2088–2097 (1975)
Tabor, M. Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989)
Berman, G. P. & Izrailev, F. M. The Fermi-Pasta-Ulam problem: fifty years of progress. Chaos 15, 015104 (2005)
Berman, G. P., Borgonovi, F., Izrailev, F. M. & Smerzi, A. Irregular dynamics in a one-dimensional Bose system. Phys. Rev. Lett. 92, 030404 (2004)
Minguzzi, A. & Gangardt, D. M. Exact coherent states of a harmonically confined Tonks-Girardeau gas. Phys. Rev. Lett. 94, 240404 (2005)
Proukakis, N. P., Schmiedmayer, J. & Stoof, H. T. C. Quasi-condensate growth on an atom chip. Preprint at http://arxiv.org/cond-mat/0509154 (2005).
Herrmann, F. & Schmalzle, P. Simple explanation of a well-known collision experiment. Am. J. Phys. 49, 761–764 (1981)
Girardeau, M. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. 1, 516–523 (1960)
Girardeau, M. D. & Wright, E. M. Measurement of one-particle correlations and momentum distributions for trapped 1D gases. Phys. Rev. Lett. 87, 050403 (2001)
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)
Rigol, M. & Muramatsu, A. Fermionization in an expanding 1D gas of hard-core bosons. Phys. Rev. Lett. 94, 240403 (2005)
Pedri, P., Santos, L., Öhberg, P. & Stringari, S. Violation of self-similarity in the expansion of a one-dimensional Bose gas. Phys. Rev. A 68, 043601 (2003)
Dunjko, V., Lorent, V. & Olshanii, M. Bosons in cigar-shaped traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between. Phys. Rev. Lett. 86, 5413–5416 (2001)
Kinoshita, T., Wenger, T. & Weiss, D. S. Local pair correlations in one-dimensional Bose gases. Phys. Rev. Lett. 95, 190406 (2005)
Gangardt, D. M. & Shlyapnikov, G. V. Stability and phase coherence of trapped 1D Bose gases. Phys. Rev. Lett. 90, 010401 (2003)
Tolra, B. L. et al. Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas. Phys. Rev. Lett. 92, 190401 (2004)
Lieb, E. H. & Liniger, W. Exact analysis of an interacting Bose gas. The general solution and the ground state. Phys. Rev. 130, 1605–1616 (1963)
Wu, S., Wang, Y. J., Diot, Q. & Prentiss, M. Splitting matter waves using an optimized standing-wave light-pulse sequence. Phys. Rev. A 71, 043602 (2005)
Wang, Y. J. et al. Atom Michelson interferometer on a chip using a Bose-Einstein condensate. Phys. Rev. Lett. 94, 090405 (2005)
Moore, M. G., Bergeman, T. & Olshanii, M. Scattering in tight atom waveguides. J. Phys. IV 116, 69–86 (2004)
Olshanii, M. Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Phys. Rev. Lett. 81, 938–941 (1998)
Wu, H. & Foot, C. J. Direct simulation of evaporative cooling. J. Phys. B 29, L321–L328 (1996)
Raman, C. et al. Evidence for a critical velocity in a Bose-Einstein condensed gas. Phys. Rev. Lett. 83, 2502–2505 (1999)
Carusotto, I. et al. Sensitive measurement of forces at the micron scale using Bloch oscillations of ultracold atoms. Phys. Rev. Lett. 95, 093202 (2005)
Fallani, L. et al. Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice. Phys. Rev. Lett. 93, 140406 (2004)
Gustavson, T. L., Landragin, A. & Kasevich, M. A. Rotation sensing with a dual atom-interferometer Sagnac gyroscope. Class. Quantum Grav. 17, 2385–2398 (2000)
Olshanii, M. & Dunjko, V. Interferometry in dense nonlinear media and interaction-induced loss of contrast in microfabricated atom interferometers. Preprint at http://arxiv.org/cond-mat/0505358 (2005).
Miesner, H.-J. et al. Bosonic stimulation in the formation of a Bose-Einstein condensate. Science 279, 1005–1007 (1998)
Kinoshita, T., Wenger, T. & Weiss, D. S. All-optical Bose-Einstein condensation using a compressible crossed dipole trap. Phys. Rev. A 71, 11602(R) (2005)
We thank M. Olshanii, K. O'Hara, K. Gibble and J. Jain for discussions, and the NSF for support.
Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.
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Kinoshita, T., Wenger, T. & Weiss, D. A quantum Newton's cradle. Nature 440, 900–903 (2006). https://doi.org/10.1038/nature04693
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