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arXiv:cond-mat/0410121 · Physical Review B

Magnetic monopoles in a charged two-condensate Bose-Einstein system

Ying Yan Jiang

Published Jul 1, 2004• 14 citations
arXivHTMLPDF

Abstract

We propose that a charged two-condensate Bose system possesses pointlike topological defects, which can be interpreted as magnetic monopoles. By making use of the $\ensuremath{\phi}$-mapping theory, the topological charges of these magnetic monopoles can be expressed in terms of the Hopf indices and Brouwer degree of the $\ensuremath{\phi}$-mapping.

DOI
10.1103/physrevb.70.012501

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•Jan 1, 2017•0 citations
We propose that a charged two-condensate Bose system possesses pointlike topological defects, which can be interpreted as magnetic monopoles. By making use of the \ensuremathϕ\ensuremath{\phi}\ensuremathϕ-mapping theory, the topological charges of these magnetic monopoles can be expressed in terms of the Hopf indices and Brouwer degree of the \ensuremathϕ\ensuremath{\phi}\ensuremathϕ-mapping.
Magnetic monopoles, which are particle-like field configurations with which one can associate a topological charge, widely exist in various three-dimensional condensate systems. In this paper, by making use of Duan 's topological current theory, we obtain the charge density of magnetic monopoles and their bifurcation theory in a charged two-condensate Bose–Einstein system. The evolution of magnetic monopoles is studied from the topological properties of a three-dimensional vector field. The magnetic monopoles are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points.
We demonstrate theoretically that, by using external magnetic fields, one can imprint pointlike topological defects on the spin texture of a dilute Bose-Einstein condensate. The symmetries of the condensate order parameter render this topological defect to be accompanied with a vortex filament corresponding to the Dirac string of a magnetic monopole. The vorticity in the condensate coincides with the magnetic field of a magnetic monopole, providing an ideal analogue to the monopole studied by Dirac.
In this paper we first derive a general method which enables one to create expressions for vortices and monopoles. By using this method we construct several order-parameters describing the vortices and monopoles of Bose–Einstein condensates with hyperfine spin F = 1 and F = 2. We concentrate on defects which are topologically stable in the absence of an external magnetic field. In particular we show that in a ferromagnetic condensate there can be a vortex which does produce any superfluid flow. We also point out that the order-parameter space of the cyclic phase of F = 2 condensate consists of two disconnected sets. Finally we examine the effect of an external magnetic field on the vortices of a ferromagnetic F = 1 condensate and discuss the experimental preparation of a vortex in this system.
Recently, an effective non-Abelian magnetic field with a topology of a monopole was shown to emerge from the adiabatic motion of multilevel atoms in spatially varying laser fields [J. Ruseckas, Phys. Rev. Lett. 95, 010404 (2005)10.1103/PhysRevLett.95.010404]. We study this monopole in a Bose-Einstein condensate of degenerate dressed states and find that the topological charge of the pseudospin cancels the monopole charge resulting in a vanishing gauge invariant charge. As a function of the laser wavelength, different stationary states are classified in terms of their effect to the monopole part of the magnetic field and a crossover to vortex ground state is observed.
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.