spin texture with a topological number skyrmion is supposed to be topologically stable;...
TRANSCRIPT
Fate of Topology in Spin-1 Spinor Bose-Einstein Con-
densate
Yun-Tak Oh, Panjin Kim, Jin-Hong Park, Jung Hoon Han,
arXiv:1309.5683
Yun-Tak Oh
Sungkyunkwan University
1. Introduction to Skyrmion texture in spin-1 BEC ( Experiments by SNU group (prof. YI Shin) )
2. Failure of the conventional classification of spin-1 BEC
3. New and complete dynamics of spin-1 BEC
CONTENTS
Skyrmion is supposed to be topologically stable;Experimentally, it is not stable!
Critical re-examination of ex-isting theory of spinor dy-namics
First successful creation of Skyrmion spin texture in spinor BEC
Shin group, PRL 108, 035301 (2012)
Spin-1 BEC classified as
Spin-spin interaction in the spin-1 condensate:
Dynamics of spin-1 BEC: Gross-Pitaevskii(GP) Equation
antiferromagnetic (AFM) for g2 > 0
ferromagnetic (FM) for g2<0
Where
Strategy: project onto three orthogonal spinors to get three hydrodynamic equations (Refael, PRB 2009)
Mass continuity eq:
Euler eq:
Landau-Lifshitz eq:
And…
No spatio-temporal fluctuation is allowed within FM mani-fold!!
In FM Limit
!
No spatio-temporal fluctuation is allowed within AFM man-ifold
with ONE EXCEPTION (next talk)
Mass continuity eq:Euler eq:
Landau-Lifshitz eq:
In AFM Limit
Again…!
Relation to Skyrmion dynamics
From homotopy consideration, stability of Skyrmion only guaranteed within AFM manifold.
However, temporal evolution within AFM manifold is in-trinsically forbidden!!
Therefore, there is no meaning to Skyrmion as a topologi-cal object.