When a system crosses a second-order phase transition on a finite timescale, spontaneous symmetry breaking can cause the development of domains with independent order parameters, which then grow and approach each other creating boundary defects. This is known as the Kibble–Zurek mechanism. Originally introduced in cosmology, it applies to both classical and quantum phase transitions, in a wide variety of physical systems. Here we report on the spontaneous creation of solitons in Bose–Einstein condensates through the Kibble–Zurek mechanism. We measure the power-law dependence of defect number on the quench time, and show that lower atomic densities enhance defect formation. These results provide a promising test bed for the determination of critical exponents in Bose–Einstein condensates.
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Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. A 9, 1387 (1976).
Kibble, T. Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980).
Zurek, W. H. Cosmological experiments in superfluid liquid helium? Nature 317, 505–508 (1985).
Zurek, W. Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177–221 (1996).
Del Campo, A., Kibble, T. W. B. & Zurek, W. H. Causality and non equilibrium second-order phase transitions in inhomogeneous systems. Preprint at http://arxiv.org/abs/1302.3648v1 (2013).
Dziarmaga, J., Smerzi, A., Zurek, W. H. & Bishop, A. R. Dynamics of quantum phase transition in an array of Josephson junctions. Phys. Rev. Lett. 88, 167001 (2002).
Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).
Bäuerle, C., Bunkov, Y. M., Fisher, S. N., Godfrin, H. & Pickett, G. R. Laboratory simulation of cosmic string formation in the early Universe using superfluid 3He. Nature 382, 332–334 (1996).
Ruutu, V. M. H. et al. Vortex formation in neutron irradiated 3He as an analogue of cosmological defect formation. Nature 382, 334–336 (1996).
Carmi, R. & Polturak, E. Search for spontaneous nucleation of magnetic flux during rapid cooling of YBa2Cu3O7−δ films through T c . Phys. Rev. B 60, 7595–7600 (1999).
Carmi, R., Polturak, E. & Koren, G. Observation of spontaneous flux generation in a multi-Josephson-junction loop. Phys. Rev. Lett. 84, 4966–4969 (2000).
Monaco, R., Mygind, J. & Rivers, R. J. Zurek–Kibble domain structures: The dynamics of spontaneous vortex formation in annular Josephson tunnel junctions. Phys. Rev. Lett. 89, 080603 (2002).
Monaco, R., Mygind, J. & Rivers, R. J. Spontaneous fluxon formation in annular Josephson tunnel junctions. Phys. Rev. B 67, 104506 (2003).
Monaco, R., Mygind, J., Rivers, R. J. & Koshelets, V. P. Spontaneous fluxoid formation in superconducting loops. Phys. Rev. B 80, 180501 (2009).
Pyka, K. et al. Symmetry breaking and topological defect formation in ion coulomb crystals. Nature Commun. 4, 2291 (2012).
Ulm, S. et al. Observation of the Kibble–Zurek scaling law for defect formation in ion crystals. Nature Commun. 4, 2290 (2013).
Ejtemaee, S. & Haljan, P. C. Spontaneous nucleation and dynamics of kink defects in zigzag arrays of trapped ions. Phys. Rev. A 87, 051401 (2013).
Zurek, W. H. Causality in condensates: Gray solitons as relics of BEC formation. Phys. Rev. Lett. 102, 105702 (2009).
Damski, B. & Zurek, W. H. Soliton creation during a Bose–Einstein condensation. Phys. Rev. Lett. 104, 160404 (2010).
Del Campo, A., Retzker, A. & Plenio, M. B. The inhomogeneous Kibble–Zurek mechanism: Vortex nucleation during Bose–Einstein condensation. J. Phys. 13, 083022 (2011).
Witkowska, E., Deuar, P., Gajda, M. & Rzą zewski, K. Solitons as the early stage of quasicondensate formation during evaporative cooling. Phys. Rev. Lett. 106, 135301 (2011).
Sabbatini, J., Zurek, W. H. & Davis, M. J. Phase separation and pattern formation in a binary Bose–Einstein condensate. Phys. Rev. Lett. 107, 230402 (2011).
Weiler, C. N. et al. Spontaneous vortices in the formation of Bose–Einstein condensates. Nature 455, 948–952 (2008).
Chen, D., White, M., Borries, C. & DeMarco, B. Quantum quench of an atomic Mott insulator. Phys. Rev. Lett. 106, 235304 (2011).
Dziarmaga, J., Tylutki, M. & Zurek, W. H. Quench from Mott insulator to superfluid. Phys. Rev. B 86, 144521 (2012).
Del Campo, A., De Chiara, G., Morigi, G., Plenio, M. B. & Retzker, A. Structural defects in ion chains by quenching the external potential: The inhomogeneous Kibble–Zurek mechanism. Phys. Rev. Lett. 105, 075701 (2010).
Donner, T. et al. Critical behavior of a trapped interacting Bose gas. Science 315, 1556–1558 (2007).
Burger, S. et al. Dark solitons in Bose–Einstein condensates. Phys. Rev. Lett. 83, 5198–5201 (1999).
Denschlag, J. et al. Generating solitons by phase engineering of a Bose–Einstein condensate. Science 287, 97–101 (2000).
Becker, C. et al. Oscillations and interactions of dark and dark-bright solitons in Bose–Einstein condensates. Nature Phys. 4, 496–501 (2008).
Chang, J. J., Engels, P. & Hoefer, M. A. Formation of dispersive shock waves by merging and splitting Bose–Einstein condensates. Phys. Rev. Lett. 101, 170404 (2008).
Shomroni, I., Lahoud, E., Levy, S. & Steinhauer, J. Evidence for an oscillating soliton/vortex ring by density engineering of a Bose–Einstein condensate. Nature Phys. 5, 193–197 (2009).
Anderson, B. P. et al. Watching dark solitons decay into vortex rings in a Bose–Einstein condensate. Phys. Rev. Lett. 86, 2926–2929 (2001).
Carr, L. D. & Brand, J. in Emergent Nonlinear Phenomena in Bose–Einstein Condensates: Theory and Experiment (eds Kevrekidis, P. G., Frantzeskakis, D. J. & Carretero-Gonzalez, R.) Ch. 7 (Springer, 2009).
Dalfovo, F. & Modugno, M. Free expansion of Bose–Einstein condensates with quantized vortices. Phys. Rev. A 61, 023605 (2000).
Ketterle, W. & van Druten, N. in Advances in Atomic, Molecular, and Optical Physics 37 (eds Bederson, B. & Walther, H.) 181–236 (1996).
Hu, H., Taylor, E., Liu, X-J., Stringari, S. & Griffin, A. Second sound and the density response function in uniform superfluid atomic gases. New J. Phys. 12, 043040 (2010).
Weir, D. J., Monaco, R., Koshelets, V. P., Mygind, J. & Rivers, R. J. Gaussianity revisited: Exploring the Kibble–Zurek mechanism with superconducting rings J. Phys. Condens. Matter Preprint at http://arxiv.org/abs/1302.7296v2 (2013).
Su, S-W., Gou, S-C., Bradley, A., Fialko, O. & Brand, J. Kibble–Zurek scaling and its breakdown for spontaneous generation of Josephson vortices in Bose–Einstein condensates. Phys. Rev. Lett. 110, 215302 (2013).
Yefsah, T. et al. Heavy solitons in a fermionic superfluid. Nature 499, 426–430 (2013).
Lamporesi, G., Donadello, S., Serafini, S. & Ferrari, G. Compact high-flux source of cold sodium atoms. Rev. Sci. Instrum. 84, 063102 (2013).
Pritchard, D. E. Cooling neutral atoms in a magnetic trap for precision spectroscopy. Phys. Rev. Lett. 51, 1336–1339 (1983).
We are indebted to L. P. Pitaevskii, I. Carusotto and A. Recati for fruitful discussions. This work is supported by Provincia Autonoma di Trento.
The authors declare no competing financial interests.
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Lamporesi, G., Donadello, S., Serafini, S. et al. Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate. Nature Phys 9, 656–660 (2013). https://doi.org/10.1038/nphys2734
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