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arXiv:1906.11453 · Physical Review Letters

Suppressing the Kibble-Zurek Mechanism by a Symmetry-Violating Bias

J. Rysti, Jere T. Mäkinen, S. Autti, T. Kamppinen, Григорий Ефимович Воловик, V. B. Eltsov

Published Sep 8, 2021• 30 citations
arXivHTMLPDF

Abstract

The formation of topological defects in continuous phase transitions is driven by the Kibble-Zurek mechanism. Here we study the formation of single- and half-quantum vortices during transition to the polar phase of ^{3}He in the presence of a symmetry-breaking bias provided by the applied magnetic field. We find that vortex formation is suppressed exponentially when the length scale associated with the bias field becomes smaller than the Kibble-Zurek length. We thus demonstrate an experimentally feasible shortcut to adiabaticity-an important aspect for further understanding of phase transitions as well as for engineering applications such as quantum computers or simulators.

DOI
10.1103/physrevlett.127.115702

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•Jan 1, 2008•1 citation
The formation of topological defects in continuous phase transitions is driven by the Kibble-Zurek mechanism. Here we study the formation of single- and half-quantum vortices during transition to the polar phase of ^{3}He in the presence of a symmetry-breaking bias provided by the applied magnetic field. We find that vortex formation is suppressed exponentially when the length scale associated with the bias field becomes smaller than the Kibble-Zurek length. We thus demonstrate an experimentally feasible shortcut to adiabaticity-an important aspect for further understanding of phase transitions as well as for engineering applications such as quantum computers or simulators.
The Kibble-Zurek mechanism predicts the formation of topological defects and other excitations that quantify how much a quantum system driven across a quantum critical point fails to be adiabatic. We point out that, thanks to the divergent linear susceptibility at the critical point, even a tiny symmetry breaking bias can restore the adiabaticity. The minimal required bias scales like τQ−βδ/(1+zν)\tau_Q^{-\beta\delta/(1+z\nu)}τQ−βδ/(1+zν)​, where β,δ,z,ν\beta,\delta,z,\nuβ,δ,z,ν are the critical exponents and τQ\tau_QτQ​ is a quench time. We test this prediction by DMRG simulations of the quantum Ising chain. It is directly applicable to the recent emulation of quantum phase transition dynamics in the Ising chain with ultracold Rydberg atoms.
The Kibble-Zurek mechanism predicts the formation of topological defects and other excitations that quantify how much a quantum system driven across a quantum critical point fails to be adiabatic. We point out that, thanks to the divergent linear susceptibility at the critical point, even a tiny symmetry breaking bias can restore the adiabaticity. The minimal required bias scales like ${\ensuremath{\tau}}_{Q}^{\ensuremath{-}\ensuremath{\beta}\ensuremath{\delta}/(1+z\ensuremath{\nu})}$, where $\ensuremath{\beta}$, $\ensuremath{\delta}$, zzz, $\ensuremath{\nu}$ are the critical exponents and ${\ensuremath{\tau}}_{Q}$ is a quench time. We test this prediction by DMRG simulations of the quantum Ising chain. It is directly applicable to the recent emulation of quantum phase transition dynamics in the Ising chain with ultracold Rydberg atoms.
In the course of a nonequilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble–Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigated the formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems. At the same time, some established results were called into question. We review and analyze the Kibble–Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.
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.
The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of pointlike topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimensions with KZM density. Numerical simulations in a one-dimensional ${\ensuremath{\phi}}^{4}$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly coupled superconductor indicating the suppression of defect-defect spatial correlations.
Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.