Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Y32: Invited Session: Recent Developments in the Kibble-Zurek Problem |
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Sponsoring Units: DCMP Room: 708-712 |
Friday, March 7, 2014 8:00AM - 8:36AM |
Y32.00001: Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking Invited Speaker: Wojciech Zurek As a result of the critical slowing down (the divergence of the relaxation time near the critical point) the dynamics of the non-equilibrium second order phase transition ceases to be adiabatic in the vicinity of the critical point. This results in a local choice of the broken symmetry of the order parameter, and can lead to the formation of topological defects. The Kibble-Zurek mechanism uses equilibrium scalings of the relaxation time and healing length in the vicinity of the critical point to describe the associated non-equilibrium dynamics of symmetry breaking and to estimate the density of topological defects as a function of the quench rate through the transition. Originally developed for classical phase transitions, it has been by now extended to quantum phase transitions (where local symmetry breaking is seeded by quantum rather than classical---e.g., thermal---fluctuations). During recent years, several new experiments investigating formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems were carried out, and more are on the way. At the same time, some established results were called into question [1]. I will review [2,3] Kibble-Zurek mechanism focusing in particular on this recent surge of activity, and suggest possible directions for further progress. \\[4pt] [1] Zurek, W. H., Topological relics of symmetry breaking: winding numbers and scaling tilts from random vortex-antivortex pairs, JOURNAL OF PHYSICS-CONDENSED MATTER Volume: 25 Issue: 40 Article Number: 404209 (2013). \\[0pt] [2] del Campo, A.; Kibble, T. W. B.; Zurek, W. H., Causality and non-equilibrium second-order phase transitions in inhomogeneous systems, JOURNAL OF PHYSICS-CONDENSED MATTER Volume: 25 Issue: 40 Article Number: 404210 (2013). \\[0pt] [3] del Campo, A.; Zurek, W. H., Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking, arXiv:1310.1600 (2013). [Preview Abstract] |
Friday, March 7, 2014 8:36AM - 9:12AM |
Y32.00002: Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate Invited Speaker: Gabriele Ferrari The Kibble-Zurek mechanism (KZM) describes the spontaneous formation of defects in systems that cross a second-order phase transition at a finite rate. The mechanism was first proposed in the context of cosmology to explain how, during the expansion of the early Universe, the rapid cooling below a critical temperature induced a cosmological phase transition resulting in the creation of domain structures. In fact, the KZM is ubiquitous in nature and regards both classical and quantum phase transitions. Experimental evidences have been observed in superfluid $^3$He, in superconducting films and rings and in ion chains. Bose-Einstein condensation in trapped dilute gases has been considered as an ideal platform for the KZM as the system is extremely clean, controllable and particularly suitable for the investigation of effects arising from the spatial inhomogeneities induced by the confinement. Quantized vortices produced in a pancake-shaped condensate by a fast quench across the transition temperature have been already observed, but their limited statistics prevented a test of the KZM scaling. The KZM has been studied across the quantum superfluid to Mott insulator transition with atomic gases trapped in optical lattices. Here we report on the observation of solitons resulting from phase defects of the order parameter, spontaneously created in an elongated Bose-Einstein condensate of sodium atoms. We show that the number of solitons in the final condensate grows according to a power-law as a function of the rate at which the transition is crossed, consistent with the expectations of the KZM, and provide the first indication of the KZM scaling with the sonic horizon. We support our observations by comparing the estimated speed of the transition front in the gas to the speed of the sonic causal horizon, showing that solitons are produced in a regime of inhomogeneous Kibble-Zurek mechanism. [Preview Abstract] |
Friday, March 7, 2014 9:12AM - 9:48AM |
Y32.00003: Universality and Dynamic Localization in Kibble-Zurek of the Quantum Ising Model Invited Speaker: Michael Kolodrubetz Recent work has suggested that the Kibble-Zurek mechanism can be re-interpreted as a theory of critical scaling out of equilibrium. While this has been shown for some classical and integrable models, in this work we demonstrate one crucial aspect of critical scaling theory: universality. We solve for the time-dependent finite-size scaling functions of the 1D transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally-studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and show that they should be robustly observable within present cold atom experiments. In addition, we discuss recent results in which the Ising model is extended by imbuing the magnetic field with dynamics. We predict using Kibble-Zurek scaling and numerically confirm that the magnetic field ramp is dynamically arrested at the quantum critical point. Extensions of this theory indicate that dynamic localization near critical points should be omnipresent in nature, and may have implications in particle physics as a possible mechanism for giving the Higgs boson a light mass. [Preview Abstract] |
Friday, March 7, 2014 9:48AM - 10:24AM |
Y32.00004: Direct observation of the proliferation of ferroelectric loop domains and vortex-antivortex pairs Invited Speaker: Seung Chae |
Friday, March 7, 2014 10:24AM - 11:00AM |
Y32.00005: Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems Invited Speaker: Vedika Khemani The classic formulation of the KZ mechanism involves phase transitions with broken symmetries. This work considers instead the the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This is interesting both as a non-trivial extension of the KZ ideas but also on account of the interest in topological phases in the theory of correlated electron systems. The work shows that the dynamics exhibits scaling in the spirit of Kibble and Zurek but now without the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. The work discusses phase transitions involving both abelian and non-abelian topological order. [Preview Abstract] |
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