Topological interactions of two-dimensional non-Abelian quantum vortices in spinor Bose–Einstein condensates

T. Mawson

Published Jan 1, 2019• 0 citations

Abstract

This thesis studies collision and braiding dynamics of types of non-Abelian vortices in ultra-cold atomic gases. It identifies a new kind of collision dynamics for these vortices with potential applications to quantum information processing and storage, as well as quantum turbulence.

DOI: 10.26180/10325735

Related papers

Braiding and Fusion of Non-Abelian Vortex Anyons

T. Mawson, Timothy C. Petersen, Johannes K. Slingerland +1 more

We have studied topology and dynamics of quantum vortices in spin-2 Bose-Einstein condensates. By computationally modeling controllable braiding and fusion of these vortices, we have demonstrated that certain vortices in such spinor condensates behave as non-Abelian anyons. We identify these anyons as fluxon, chargeon, and dyon quasiparticles. The pertinent anyon models are defined by the quantum double of the underlying discrete non-Abelian symmetry group of the condensate ground state order parameter.

arXiv:1805.10009Physical Review LettersOct 3, 201926 citations

Collision dynamics of two-dimensional non-Abelian vortices

T. Mawson, Timothy C. Petersen, Tapio Simula

We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation---an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.

arXiv:1705.10919Physical Review ASep 18, 20172 citations

Physics of non-Abelian vortices in Bose-Einstein condensates

Michikazu Kobayashi

A wide order-parameter manifolds of Bose-Einstein condensates (BECs) with spin degrees of freedom enables various kinds of topological defects which never appear in conventional scalar BECs. In this paper, we focus on the characteristic example of them; non-Abelian vortices and their dynamics in the cyclic phase of a spin-2 BEC. Non-Abelian vortices shows the unique effect in their collision dynamics, i.e. unlike Abelian vortices, they do neither reconnect themselves nor pass through each other but create a rung vortex between them.

Journal of Physics Conference SeriesMay 1, 20114 citations

Topological Excitations in Spinor Bose-Einstein Condensates

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.

arXiv:1006.5839Progress of Theoretical Physics SupplementOct 1, 201026 citations

Collision Dynamics and Rung Formation of non-Abelian Vortices

Michikazu Kobayashi, Yuki Kawaguchi, Muneto Nitta +1 more

We investigate the collision dynamics of two non-Abelian vortices and find that, unlike Abelian vortices, they neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. Our predictions are verified using the model of the cyclic phase of a spin-2 spinor Bose-Einstein condensate.

arXiv:0810.5441Physical Review LettersSep 8, 200998 citations

Rungihilation of non-Abelian vortices

T. Mawson, Timothy C. Petersen, Tapio Simula

We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation - an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.

May 31, 20170 citations