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arXiv:cond-mat/0106301 · Physical Review Letters

Creation of a Monopole in a Spinor Condensate

J.-P. Martikainen, Anssi Collin, Kalle‐Antti Suominen

Published Feb 14, 2002• 37 citations
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Abstract

We propose a method to create a monopole structure in a multicomponent condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We also show that by using a two-component structure for a monopole, we can avoid many problems related to the previously suggested three-component monopole. We discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.

DOI
10.1103/physrevlett.88.090404

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•Jan 1, 2019•0 citations
We propose a method to create a monopole structure in a multicomponent condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We also show that by using a two-component structure for a monopole, we can avoid many problems related to the previously suggested three-component monopole. We discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.
We present a method for creating a monopole in an antiferromagnetic spin-1 Bose-Einstein condensate. The required phase engineering of the multicomponent condensate is achieved using light shifts, which depend on both the magnetic substate mF{m}_{F}mF​ and polarization of the incident laser beam.
Magnetic monopoles are crucial in explaining the quantization of electric charges and quantum Hall effects, while artificially creating a minimal magnetic monopole in experiments remains a challenge. Here we develop a flexible way to simulate a half-integer-type monopole in Bose gases and investigate the induced vortex dynamics on a sphere. We list the possible experiment parameter settings for different isotopes and discuss their experimental feasibility. With the assumption of a rigid monopole-vortex structure, we analytically predict the vortex trajectory in an external magnetic field. We then confirm the result by numerically solving the Gross-Pitaevskii equation, which employs two gauges simultaneously (the Wu-Yang approach) to prevent singularity in the one-gauge method when a monopole is present. The study offers significant insight into the characteristics of monopoles and vortices, facilitating avenues for experimental validation.
A rich variety of order parameter manifolds of multicomponent Bose-Einstein condensates (BECs) admit various kinds of topological excitations, such as fractional vortices, monopoles, skyrmions, and knots. In this paper, we discuss two topological excitations in spinor BECs: non-Abelian vortices and knots. Unlike conventional vortices, non-Abelian vortices neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. We discuss the collision dynamics of non-Abelian vortices in the cyclic phase of a spin-2 BEC. In the latter part, we show that a knot, which is a unique topological object characterized by a linking number or a Hopf invariant [π3 (S2) = Z], can be created using a conventional quadrupole magnetic field in a cold atomic system.
Bose–Einstein condensation is a quantum statistical phase transition that occurs in a system consisting of bosons when a single-particle quantum state becomes macroscopically occupied. This peculiar state of matter was first predicted in 1925 and finally realized seventy years later in vapours of weakly-interacting alkali-metal atoms. Since then, Bose–Einstein condensates have been one of the most fascinating research fields in modern physics. \n \nThe gaseous condensates offer a robust platform to accurately study interacting many-particle systems from the first principles. Experimentally, the possibility to precisely control a condensate with external fields and directly image its order parameter provides unforeseen opportunities to obtain deep insight into phenomena across different subfields of physics. In particular, gaseous condensates can emulate complicated models that arise in atomic, condensed-matter, and even particle physics, allowing realizations of exotic phenomena that are elusive in their original contexts. An outstanding example is the existence of various topological defects in ultacold quantum gases with internal degrees of freedom. \n \nIn this thesis, we investigate the creation, stability, and dynamical properties of various topological defects in spinor Bose–Einstein condensates. The majority of the theoretical results is obtained by numerically solving the dynamics using Gross–Pitaevskii equations for spin-1 condensates. Many theoretical predictions are confirmed by the very good agreement with experiments. \n \nThe first experimental observations of a topological point defect in an order parameter describing the quantum gas are presented. Such a point defect is reminiscent to the magnetic monopole particle appearing in grand unified theories. Therefore, the discovery of monopoles in quantum gases further encourages the quest for finding magnetic monopoles in natural electromagnetic fields, a search largely initiated by Paul Dirac almost a century ago. \n \nSubsequently, the fine structure and decay dynamics of the point defect are studied numerically and verified in experiments. The created monopole is gradually destroyed during the polar-to-ferromagnetic quantum phase transition, which results in the spontaneous emergence of a Dirac monopole in synthetic magnetic field. In addition to the singular point defect, the first experimental realization of a knot soliton in the context of quantum field is reported. This thesis lays the foundation for studies of the dynamics and stability of three-dimensional topological structures in quantum systems.
Topology provides deep conceptual links between the various branches of physics. Bose–Einstein condensates with spin degrees of freedom are among the most accessible quantum systems available for studying topological structures. A wide range of topological defects and textures available in condensates, such as vortices, monopoles, knots, and skyrmions, are analogous to those predicted in electromagnetism, high-energy physics, and cosmology. In this dissertation, we numerically and experimentally investigate novel creation methods for topological structures and study their dynamical properties. Specifically, we experimentally observe the evolution of an isolated monopole into a Dirac monopole in the presence of a quadrupole magnetic field. The Dirac monopole appears in the synthetic magnetic field of the condensate and is accompanied by spontaneously emerging nodal lines. We observe the decay of a quantum knot into a polar-core spin vortex in the presence of a uniform magnetic field. Furthermore, we observe that a decaying coreless-vortex state gives rise to a pair of singular SO(3) vortices. Many of the studied creation methods for topological structures in the condensate rely on adiabatic control of the external magnetic field. The counterdiabatic protocol offers a way to speed up the otherwise slow magnetic field driving required for adiabatic dynamics with a correcting magnetic field. Using this method, we numerically implement a scheme for fast vortex pumping which leads to the vortex with highest angular momentum reported to date in Bose–Einstein condensates with experimentally feasible methods. We further use the counterdiabatic protocol in a novel way to create quantum knots in the condensate. Another focal point of this dissertation is the study on different types of skyrmions in spinor condensates. Our simulations of two-dimensional skyrmions are in a quantitative agreement with an experiment carried out elsewhere, explaining the experimentally observed instabilities. We numerically analyze the exotic spin-2 skyrmions available in the cyclic and biaxial nematic phases. Importantly, we present the first experimental observations of Shankar skyrmions in spin-1 condensates and analyze their synthetic electromagnetic properties. This dissertation addresses an extensive amount of topological structures available in the condensate, but many different structures await future studies. In addition, the precise computational characterization of the elementary excitations of monopoles, knots, and skyrmions is of great interest. The results of this dissertation form a sturdy basis for future experimental studies on the dynamics of topological structures in spinor condensates.; Topologia tarjoaa syvallisia kasitteellisia yhteyksia fysiikan eri haarojen valilla. Bosen–Einsteinin kondensaatit spin-vapausasteilla ovat yksia monipuolisimmista systeemeista topologisten rakenteiden tutkimukseen. Laaja kirjo kondensaatissa esiintyvia topologisia rakenteita, kuten kvanttipyorteet, monopolit, solmut ja skyrmionit, ovat…