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A quantum Newton's cradle


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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Figure 1: Classical and quantum Newton's cradles.
Figure 2: Absorption images in the first oscillation cycle for initial average peak coupling strength γ o = 1.
Figure 3: The expanded momentum distribution, f(pex), for three values of γo.
Figure 4: Projected versus actual f(pex) for various γd, the dephased average peak coupling strength.


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We thank M. Olshanii, K. O'Hara, K. Gibble and J. Jain for discussions, and the NSF for support.

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Correspondence to David S. Weiss.

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Reprints and permissions information is available at The authors declare no competing financial interests.

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Supplementary Data

Contains Supplementary Fig. SI1 and SI2, their legends and notes on the observation of heating, and fine spatial structure. (DOC 381 kb)

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Kinoshita, T., Wenger, T. & Weiss, D. A quantum Newton's cradle. Nature 440, 900–903 (2006).

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