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arXiv:cond-mat/0105187

Testing the Zurek-Kibble Causality Bounds with Annular Josephson Tunnel Junctions

R. Monaco, R. J. Rivers, E. Kavoussanaki

Published May 9, 2001• 0 citations
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Abstract

Zurek has provided simple causal bounds for the onset of phase transitions in condensed matter, that mirror those proposed by Kibble for relativistic quantum field theory. In this paper we show how earlier experiments with annular Josephson tunnel Junctions are consistent with this scenario, and suggest how further experiments might confirm it.

DOI
10.48550/arxiv.cond-mat/0105187

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•May 1, 2018•0 citations
Zurek has provided simple causal bounds for the onset of phase transitions in condensed matter, that mirror those proposed by Kibble for relativistic quantum field theory. In this paper we show how earlier experiments with annular Josephson tunnel Junctions are consistent with this scenario, and suggest how further experiments might confirm it.
If systems change as fast as possible as they pass through a phase transition then the initial domain structure is constrained by causality. We shall show how we can trace these causal horizons by measuring the spontaneous production of flux in annular Josephson Tunnel Junctions as a function of the quench time τQτ_{Q}τQ​ into the superconducting phase. A specific test of our analysis is that the probability P1_{1}1​ to trap a single fluxon at the N-S transition clearly follows an allometric dependence on τQτ_{Q}τQ​ as P1=aτQ−σP_1 = a τ_Q^{-σ}P1​=aτQ−σ​, with a scaling exponent σ=0.25σ= 0.25σ=0.25, in agreement with the data.
Systems passing through quantum critical points at finite rates have a finite probability of undergoing transitions between different eigenstates of the instantaneous Hamiltonian. This mechanism was proposed by Kibble as the underlying mechanism for the formation of topological defects in the early universe and by Zurek for condensed matter systems. Here, we use a system of nuclear spins as an experimental quantum simulator undergoing a non-equilibrium quantum phase transition. The experimental data confirm the validity of the Kibble–Zurek mechanism of defect formation.
Abstract Out-of-equilibrium phenomena are a subject of considerable interest in many fields of physics. Ultracold quantum gases, which are extremely clean, well-isolated and highly controllable systems, offer ideal platforms to investigate this topic. The recent progress in tailoring trapping potentials now allows the experimental production of homogeneous samples in custom geometries, which is a key advance for studies of the emergence of coherence in interacting quantum systems. Here we review recent experiments in which temperature quenches have been performed across the Bose–Einstein condensation phase transition in an annular geometry and in homogeneous 3D and quasi-2D gases. Combined, these experiments comprehensively explore and validate the Kibble–Zurek (KZ) scenario through complementary measurements of correlation functions and density of topological defects. They allow the measurement of KZ scaling laws, the direct confirmation of the ‘freeze-out’ hypothesis that underlies the KZ theory, and the extraction of critical exponents of the Bose–Einstein condensation transition.
Atomic Bose-Einstein condensates confined to a dual-ring trap support Josephson vortices as topologically stable defects in the relative phase. We propose a test of the scaling laws for defect formation by quenching a Bose gas to degeneracy in this geometry. Stochastic Gross-Pitaevskii simulations reveal a -1/4 power-law scaling of defect number with quench time for fast quenches, consistent with the Kibble-Zurek mechanism. Slow quenches show stronger quench-time dependence that is explained by the stability properties of Josephson vortices, revealing the boundary of the Kibble-Zurek regime. Interference of the two atomic fields enables clear long-time measurement of stable defects and a direct test of the Kibble-Zurek mechanism in Bose-Einstein condensation.
The dynamics of a quantum phase transition are explored using slow quenches from the polar to the broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. Measurements of the evolution of the spin populations reveal a power-law scaling of the temporal onset of excitations versus quench speed as predicted from quantum extensions of the Kibble-Zurek mechanism. The satisfactory agreement of the measured scaling exponent with the analytical theory and numerical simulations provides experimental confirmation of the quantum Kibble-Zurek model.
The Kibble Zurek mechanism describes the universal formation of topological defects during continuous symmetry breaking phase transitions. It has been confirmed in a wide variety of systems and is of interest within theoretical high energy physics and cosmology. While during high temperature phase transitions classical methods can be used to study topological defect formation, in zero temperature quantum phase transitions, quantum effects can dominate dynamics such that classical approximations fail. This is problematic in quantum field theory because topological defect formation constitutes a non-perturbative non-equilibrium phenomenon, yet there are at present no well-developed non-perturbative non-equilibrium methods available for calculations. Nonetheless, due to its generality and confirmation in other cases, the Kibble-Zurek mechanism is expected to hold. This means that in addition to being of physical interest in its own right, the Kibble-Zurek mechanism is also an excellent test for any potential non-perturbative non-equilibrium techniques. In this thesis, tensor network techniques are applied to the problem of confirming the Kibble Zurek mechanism in the phi^4 quantum field theory in D = (1 + 1) spacetime dimensions. Such techniques have already been highly successful in condensed matter and to some extent in quantum field theory. The kink defects of the theory are studied both in equilibrium and in the non-equilibrium scenario of their formation. Results consistent with the Kibble-Zurek mechanism are found, which provides evidence that the mechanism holds in this case and confirms tensor networks as a promising non-perturbative non-equilibrium method for quantum field theory. As tensor network methods are developed further to higher dimensions and more sophisticated theories, they could one day provide a powerful method for the non-perturbative study of non-equilibrium high energy physics and cosmology, an area of physics which remains essentially unexplored yet important for our understanding of nature.