Yurii V Dumin 2009 New J. Phys. 11 103032 doi:10.1088/1367-2630/11/10/103032
Ultracold gases and multi-Josephson junctions as simulators of out-of-equilibrium phase transformations in superfluids and superconductors
Yurii V Dumin1
Show affiliationsThe experiments on strongly nonequilibrium symmetry-breaking phase transformations in superfluids and superconductors revealed that the topological defects (e.g. vortices) are produced most efficiently in the systems of microscopic size or low dimensionality (D=1), while in the macroscopic two-dimensional (2D) and 3D samples the efficiency of their formation was substantially suppressed (by a few orders of magnitude) as compared to theoretical predictions. A reasonable explanation for this behaviour is based on the specific thermal correlations between the phases of Bose–Einstein condensates formed in the spatial subregions disconnected during the phase transformation. Such correlations were initially revealed in the multi-Josephson-junction loop experiment (Carmi R et al 2000 Phys. Rev. Lett. 84 4966) and were confirmed recently by the experiments with ultracold atoms in periodic potentials (Hadzibabic Z et al 2006 Nature 441 1118). We begin our theoretical consideration from a phase transformation in the simplest 
4-model of the real scalar field and show that, under the presence of the above-mentioned correlations, the final symmetry-broken states are described by the effective Ising model. Its behaviour changes dramatically in passing from finite to infinite size of the system and from the low (D=1) to higher (D≥2) dimensionality, which is in qualitative agreement with the experimental results.
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GENERAL SCIENTIFIC SUMMARY
Introduction and background. Formation of topological defects (such as the monopoles, strings (vortices), and domain walls) should be a common feature of all strongly nonequilibrium symmetry-breaking phase transformations, ranging from the condensed matter in the laboratory (e.g. superfluids, superconductors, liquid crystals etc.) to the fundamental fields at the early stages of cosmological evolution. However, the measured numbers of the defects are usually much less than theoretical predictions, apart from the microscopic and quasi-one-dimensional samples.Main results. To explain the available laboratory data on the defect formation in superfluids and superconductors, we employ the recent observations of phase mismatch in the interfering ultracold gases and multi-Josephson junctions experiencing a rapid phase transformation. Both of these systems show the pronounced residual thermal correlations between the phases of order parameter in the spatial subregions disconnected during the transformation, thereby reducing creation of the stable topological defects. As follows from our model estimates, this effect should be especially prominent in the macroscopic samples of dimensionality greater than unity (see figure), which is in qualitative agreement with experimental findings.
Wider implications. Apart from the condensed-matter applications, our approach can be used also to explain the lack of the monopoles and cosmic strings, predicted after the phase transitions in the early Universe.
Figure. Concentration of the defects (domain walls) n in our model normalized to the standard (the so-called Kibble–Zurek) prediction nKZ as a function of the ratio of the defect energy E to the phase transition temperature Tc. It is seen that the reduction of the defect formation is not so great for a one-dimensional (1D) system (dashed green curve), but increases for a microscopic 2D system (dotted blue curve) and becomes dramatic for the macroscopic 2D system (solid red curve). - PACS
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74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects
67.30.he Textures and vortices
74.62.-c Transition temperature variations
67.25.dk Vortices and turbulence
- Subjects
- Dates
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Issue 10 (October 2009)
Received 5 August 2009
Published 21 October 2009
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Ultracold gases and multi-Josephson junctions as simulators of out-of-equilibrium phase transformations in superfluids and superconductors
Yurii V Dumin 2009 New J. Phys. 11 103032
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