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Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas

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Science  09 Jan 2015:
Vol. 347, Issue 6218, pp. 167-170
DOI: 10.1126/science.1258676
  • Fig. 1 Domain formation during spontaneous symmetry breaking in a homogeneous Bose gas.

    (A) Red points depict thermal atoms and blue areas coherent domains, in which the Embedded Image gauge symmetry is spontaneously broken. The arrows indicate the independently chosen condensate phase at different points in space, and dashed lines delineate domains over which the phase is approximately constant. The average size Embedded Image of the domains formed at the critical point depends on the cooling rate. Further cooling can increase the population of each domain before the domain boundaries evolve. (B) Phase inhomogeneities in a deeply degenerate gas are revealed in TOF expansion as density inhomogeneities. Shown are three realizations of cooling the gas in 1 s from Embedded ImagenK, through Embedded ImagenK, to Embedded Image nK. Each realization of the experiment results in a different pattern, and averaging over many images results in a smooth, featureless distribution. (C) Preparing a Embedded ImagenK gas more slowly (over 5 s) results in an essentially pure BEC with a spatially uniform phase.

  • Fig. 2 Two-point correlation functions in equilibrium and quenched gases.

    (A) Homodyne interferometric scheme. The first Bragg-diffraction pulse (Embedded Image) creates a superposition of a stationary cloud and its copy moving with a center-of-mass velocity Embedded Image. After a time Embedded Image, a second pulse is applied. In the region where the two copies of the cloud displaced by Embedded Image overlap, the final density of the diffracted atoms depends on the relative phase of the overlapping domains; Embedded Image is deduced from the diffracted fraction Embedded Image (see text). (B) Correlation function Embedded Image measured in equilibrium (blue) and after a quench (red) for, respectively, two different Embedded Image values and two different quench times. (Inset) 1D calculation of Embedded Image for a fragmented BEC containing Embedded Image (red) and Embedded Image (light red) domains of random sizes and phases. The solid lines correspond to Embedded Image.

  • Fig. 3 KZ scaling and freeze-out hypothesis.

    (A) Quench protocols. The self-similar QP1 trajectories are shown in blue for total cooling time Embedded Image s (upper panel) and Embedded Image s (lower panel). We use polynomial fits to the data (solid lines) to deduce Embedded Image and Embedded Image. QP2 is shown in the lower panel by the orange points, with the kink at Embedded Image. (B) Coherence length Embedded Image as a function of Embedded Image. Blue points correspond to QP1. The shaded blue area shows power-law fits with Embedded Image to the data with Embedded Image s. The horizontal dotted line indicates our instrumental resolution. (C) Coherence length Embedded Image measured following QP2, as a function of Embedded Image, for Embedded Image s (orange), Embedded Image s (green), and Embedded Image s (purple). The shaded areas correspond to the essentially constant Embedded Image (and its uncertainty) in the freeze-out period Embedded Image. (For Embedded Image the system never unfreezes.) The (average) Embedded Image values within these plateaus are shown in their respective colors as diamonds in (B).

  • Fig. 4 Critical exponents of the interacting BEC transition.

    Orange circles and diamonds show Embedded Image values obtained using QP2, as in Fig. 3C; the diamonds show the same three data points as in Fig. 3B. Blue circles show the same QP1 data, with Embedded Image s as in Fig. 3B. We obtained Embedded Image (solid line), in agreement with the F-model prediction Embedded Image, corresponding to Embedded Image and Embedded Image, and excluding the mean-field value Embedded Image.

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  • Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas

    Nir Navon, Alexander L. Gaunt, Robert P. Smith, Zoran Hadzibabic

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