Fate of Topology in Spin-1 Spinor Bose-Einstein Condensate

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## Fate of Topology in Spin-1 Spinor Bose-Einstein Condensate

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**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)