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Spontaneous creation of solitons by shock cooling sodium Bose-Einstein condensates

M.A. van Gogh

Published Feb 11, 2015• 0 citations
OpenAlex

Abstract

We study the formation of defects in a Bose-Einstein condensate as is described by the Kibble-Zurek mechanism. The mechanism describes the formation of defects when a second order phase transition is crossed at a finite rate. This is done by shock cooling or quenching the last part of the evaporative cooling process where the transition into the condensed state is made. This allows for the study of the amount of solitons formed as a function of the quench time with the ultimate goal of determining the critical exponents of the phase transition. The amount of solitons is predicted by the Kibble-Zurek mechanism to scale as the quench time to the power alpha, which we attempted to measure. The dynamics of solitons are also studied in order to determine the time scale on which they decay. This turns out to be in the order of 0.29 seconds, and thus an important factor, since we consider quench times in the order of seconds. When correcting for the decay on this timescale, it turns out that alpha is extremely sensitive to variations in the decay time and therefore we were not able to give conclusive evidence on a value for the exponent. Instead we estimate the value of alpha to be between 0.5 and 2, based on our measurements.

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We study the formation of defects in a Bose-Einstein condensate as is described by the Kibble-Zurek mechanism. The mechanism describes the formation of defects when a second order phase transition is crossed at a finite rate. This is done by shock cooling or quenching the last part of the evaporative cooling process where the transition into the condensed state is made. This allows for the study of the amount of solitons formed as a function of the quench time with the ultimate goal of determining the critical exponents of the phase transition. The amount of solitons is predicted by the Kibble-Zurek mechanism to scale as the quench time to the power alpha, which we attempted to measure. The dynamics of solitons are also studied in order to determine the time scale on which they decay. This turns out to be in the order of 0.29 seconds, and thus an important factor, since we consider quench times in the order of seconds. When correcting for the decay on this timescale, it turns out that alpha is extremely sensitive to variations in the decay time and therefore we were not able to give conclusive evidence on a value for the exponent. Instead we estimate the value of alpha to be between 0.5 and 2, based on our measurements.
When a second-order phase transition is crossed at finite speed, domains with independent order parameters can appear in the system, with the consequent formation of defects at the domain boundaries. The Kibble-Zurek theory provides a description for this universal phenomenon, which applies to many different systems in nature, and it predicts a power-law dependence of the defect density on the quench rate. This thesis reports on the results of the experimental study of the Kibble-Zurek mechanism in elongated Bose-Einstein condensates of atomic sodium gases, following the observations on the spontaneous formation of defects after temperature quenches across the BEC transition. The power-law scaling of the defect number with the quench speed was observed and characterized for the first time in ultracold gases. The characterization of the density and phase profiles of the defects allowed their identification as solitonic vortices, representing the first direct experimental evidence for this kind of long living excitation, which sets a link between solitons and vortices. The measurements reported in this thesis provide a novel approach to the study of the critical phenomena happening at phase transitions, and introduce to the possibility of exploring the turbulent dynamics of quenched systems through the spontaneous production of solitonic vortices.
The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.
Continuous phase transitions occur in a wide range of physical systems, and provide a context for the study of non-equilibrium dynamics and the formation of topological defects.The Kibble-Zurek (KZ) mechanism predicts the scaling of the resulting density of defects as a function of the quench rate through a critical point, and this can provide an estimate of the critical exponents of a phase transition.In this work we extend our previous study of the miscible-immiscible phase transition of a binary Bose-Einstein condensate (BEC) composed of two hyperfine states in which the spin dynamics are confined to one dimension [J.Sabbatini et al., Phys.Rev. Lett.107, 230402 (2011)].The transition is engineered by controlling a Hamiltonian quench of the coupling amplitude of the two hyperfine states, and results in the formation of a random pattern of spatial domains.Using the numerical truncated Wigner phase space method, we show that in a ring BEC the number of domains formed in the phase transitions scales as predicted by the KZ theory.We also consider the same experiment performed with a harmonically trapped BEC, and investigate how the density inhomogeneity modifies the dynamics of the phase transition and the KZ scaling law for the number of domains.We then make use of the symmetry between inhomogeneous phase transitions in anisotropic systems, and an inhomogeneous quench in a homogeneous system, to engineer coupling quenches that allow us to quantify several aspects of inhomogeneous phase transitions.In particular, we quantify the effect of causality in the propagation of the phase transition front on the resulting formation of domain walls, and find indications that the density of defects is determined during the impulse to adiabatic transition after the crossing of the critical point.
Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point ("critical slowing down"). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains - fragments of broken symmetry - and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth - both experimentally measurable - follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition.
We study the spontaneous formation of defects in the order parameter of a trapped ultracold bosonic gas while crossing the critical temperature for Bose-Einstein condensation at different rates. The system has the shape of an elongated ellipsoid, whose transverse width can be varied. For slow enough temperature quenches we find a power-law scaling of the average defect number with the quench rate, as predicted by the Kibble-Zurek mechanism. A breakdown of such a scaling is found for fast quenches, leading to a saturation of the average defect number. We suggest an explanation for this saturation in terms of the mutual interactions among defects.