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Quantum Electronics and Laser Science Conference

Non topological vortices in a Bose-Einstein condensate

Q‐Han Park, Joseph H. Eberly

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. Vortex in a BEC is a circular flow with a quantized angular momentum. In a two-component BEC, the internal phase space can be enlarged to two sphere so that non topological vortices carrying continuous angular momentum are possible. In this talk, we present a novel class of non topological vortices and describe their rich static and dynamical properties. Each components of these non topological vortices can possess rich spatial structures while their total intensities have simple radial profiles similar to those of conventional topological vortices. These vortices carry continuous angular momenta varying between two integer momentum numbers m and -m, whose physical meaning will be explained in the Poincare sphere picture Particularly, we show that external drive can be coupled easily to a non topological vortex and be used to steer a vortex which sets internal spinor motions. We also make an experimental suggestion for a method to create such nontopological vortices.

DOI
10.1109/qels.2002.1031244

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Summary form only given. Vortex in a BEC is a circular flow with a quantized angular momentum. In a two-component BEC, the internal phase space can be enlarged to two sphere so that non topological vortices carrying continuous angular momentum are possible. In this talk, we present a novel class of non topological vortices and describe their rich static and dynamical properties. Each components of these non topological vortices can possess rich spatial structures while their total intensities have simple radial profiles similar to those of conventional topological vortices. These vortices carry continuous angular momenta varying between two integer momentum numbers m and -m, whose physical meaning will be explained in the Poincare sphere picture Particularly, we show that external drive can be coupled easily to a non topological vortex and be used to steer a vortex which sets internal spinor motions. We also make an experimental suggestion for a method to create such nontopological vortices.
Abstract Chapter 4 addresses the progress of studies on superfluid dynamics, mainly related to the dynamics of quantized vortices, in cold-atom BECs. First, we give a minimal description of the physics of cold atoms, e.g. cooling, trapping, control of interatomic interactions by external fields. We then turn to the argument of superfluid hydrodynamics in a scalar BEC characterized by a single-component order parameter. The properties of the vortices can be well described on the basis of the GP model, which allows a quantitative comparison between theory and experiment. We will discuss topics such as single vortex dynamics, interacting dynamics of a few vortices, vortex lattice formation in a rotating BEC, and collective properties of a vortex lattice in a rapidly rotating BEC, which have been unraveled experimentally by direct visualization of vortices in condensed gases. Next, we will discuss the properties of vortices in multicomponent BECs characterized by the multicomponent order parameters. We will first explain the vortex physics in two-component BECs as a simple case, finding that their structures and dynamics are highly nontrivial due to the presence of the intercomponent interaction; we will cover the topics of vortex structure composed of two-component order parameters, dynamics of composite vortices, exotic vortex lattices, and hydrodynamic instabilities associated with the interface dynamics between immiscible condensates. Finally, we explain the vortices in a spinor BEC. The vortex structures are extremely rich due to the complicated order parameter manifold, which is clarified by the discussion on vortices in spin-1 and spin-2 spinor BECs.
We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac BEC) described by a stationary Dirac Gross-Pitaevskii equations (GPE). We find that the multi-component structure of Dirac equation enables the difference in phase winding of two condensates with respective phase winding number differing by one, ℓa−ℓb=±1\ell_a - \ell_b = \pm 1ℓa​−ℓb​=±1. We observe three classes of vortex states distinguished by their far-field behavior: A ring soliton on either of the two components in combination with a vortex on the other component, and, in the case of strong inter-component interactions, a vortex profile on both components. The latter are multiple core vortices due to the phase winding difference between the components. We also address the role of a Haldane gap on these vortices, which has a similar effect than inter-component by making the occupation on either sublattice more costly. We employ a numerical shooting method to reliably identify vortex solutions and use it to scan large parts of the phase space. We then use a classification algorithm on the integrated wavefunctions to establish a phase diagram of the different topological sectors.
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.
While quantized vortices and vortex lattices in Bose-Einstein condensates (BECs) have received much recent attention, the formation and dynamics of vortex dipoles have been nearly unexplored in experimental BECs. Vortex dipoles consist of a pair of vortices of opposite circulation moving under the influence of each other, and may be considered as metastable topological structures that carry linear momentum in a fluid. In this talk, a collaborative experimental and numerical study of the formation, dynamics, and lifetimes of vortex dipoles in BECs will be presented. In our work [1], single vortex dipoles were deterministically nucleated by causing highly oblate, harmonically trapped BECs to move past a repulsive obstacle above a supercritical flow velocity. Our measured critical velocity for vortex dipole shedding, and the subsequent dipole dynamics, are in good agreement with new numerical simulations. We find that vortex dipoles can survive for many seconds in the BEC without selfannihilation, and that multiply charged vortex dipoles can be formed with high enough flow velocities. References: 1. T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, and B.P. Anderson, preprint available at http://arxiv.org/abs/0912.3773.