Topological Structure of Vortices in Multicomponent Bose-Einstein Condensates

Xu Tao

The structure of the vortex in a two-component Bose—Einstein condensate is studied by the method of Dirac δ function. The vortex can be characterized by the Brouwer degree and Hopf index, i.e., β 1 η 1 , β 2 η 2 . The circulation of the vortex can be a fraction, which is different from the usual result for a one-component condensate. The kinetic helicity of vortices is calculated.

正仁 上田, Masahito Ueda

Yuki Kawaguchi, Michikazu Kobayashi, Muneto Nitta +1 more

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.

S. Bargi, J. Christensson, G. M. Kavoulakis +4 more

Fanghua Lin, Tai‐Chia Lin

Roberto Zamora-Zamora, M. Lozada-Hidalgo, Santiago F. Caballero-Benítez +1 more

We present a simple mechanism to produce vortices at any desired spatial locations in harmonically trapped Bose-Einstein condensates (BECs) with multicomponent spin states coupled to external transverse and axial magnetic fields. The vortices appear at the spatial points where the spin-transverse field interaction vanishes and, depending on the multipolar magnetic field order, the vortices can acquire different predictable topological charges. We explicitly demonstrate our findings, both numerically and analytically, by analyzing a 2D BEC via the Gross-Pitaevskii equation for atomic systems with either two or three internal states. We further show that by a spontaneous symmetry-breaking mechanism, vortices can appear in any spin component, unless symmetry is externally broken at the outset by an axial field. We suggest that this scenario may be tested using an ultracold gas of ${}^{87}$Rb occupying all three $F=1$ states in an optical trap.