Fate of Topology in Spin-1 Spinor Bose-Einstein Condensate Yun-Tak Oh Sungkyunkwan University Yun-Tak Oh, Panjin Kim, Jin-Hong Park, Jung Hoon Han, arXiv:1309.5683
CONTENTS 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
What is a Skyrmion? Spin texture with a topological number
First successful creation of Skyrmion spin texture in spinor BEC Skyrmion is supposed to be topologically stable; Experimentally, it is not stable! Critical re-examination of existing theory of spinor dynamics Shin group, PRL 108, 035301 (2012)
Dynamics of spin-1 BEC: Gross-Pitaevskii(GP) Equation Spin-spin interaction in the spin-1 condensate: Spin-1 BEC classified as ferromagnetic (FM) for g2<0 antiferromagnetic (AFM) for g2 > 0 Where
Spin-1 BEC FM AFM : Initial state Implicitly assumed dynamics occur within AFM or FM manifold
Strategy: project onto three orthogonal spinors to get three hydrodynamic equations (Refael, PRB 2009)
In FM Limit Mass continuity eq: Euler eq: Landau-Lifshitzeq: ! And… No spatio-temporal fluctuation is allowed within FM manifold!!
In AFM Limit Mass continuity eq: Euler eq: Landau-Lifshitzeq: Again…! No spatio-temporal fluctuation is allowed within AFM manifold with ONE EXCEPTION (next talk)
Spin-1 BEC FM AFM All dynamics involves evolution into a mixed state (δ ≠ 0)
Relation to Skyrmion dynamics From homotopy consideration, stability of Skyrmion only guaranteed within AFM manifold. However, temporal evolution within AFM manifold is intrinsically forbidden!! Therefore, there is no meaning to Skyrmion as a topological object.
Conclusion: • Initially tried to understand unstable Skyrmion dynamics • Instead found neither AFM nor FM sub-manifold supports a well-define d dynamics • (FM; t=0) (FM+AFM, t>0) • (AFM; t=0) (AFM+FM, t>0) • Numerical solution of the Gross-Pitaevskii equation proves our claim (next talk)