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Panjin Kim Department of Physics Sungkyunkwan University October 31, 2013

Fate of Topology in Spin-1 Spinor Bose-Einstein Condensate: Temporal Dynamics. Panjin Kim Department of Physics Sungkyunkwan University October 31, 2013. Yun-Tak Oh, Panjin Kim, Jin-Hong Park, and Jung Hoon Han, arXiv : 1309.5683. Conclusion from the previous talk.

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Panjin Kim Department of Physics Sungkyunkwan University October 31, 2013

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  1. Fate of Topology in Spin-1 Spinor Bose-Einstein Condensate: Temporal Dynamics Panjin Kim Department of Physics Sungkyunkwan University October 31, 2013 Yun-Tak Oh, Panjin Kim, Jin-Hong Park, and Jung Hoon Han, arXiv: 1309.5683

  2. Conclusion from the previous talk • Neither antiferromagnetic (AFM) nor ferromagnetic (FM) sub-manifold supports temporal dynamics of spin-1 Bose-Einstein condensate (BEC). • Except a very few cases, purely AFM or FM initial state soon evolves into mixture of AFM and FM state.

  3. Contents • Numerical solution of Gross-Pitaevskii (GP) equation in one- and two-dimensions • One example of sustainable dynamics within the AFM manifold

  4. Gross-Pitaevskii equation • GP equation has the form of the Schrödinger equation with the addition of interaction terms. • : atomic mass • : frequency of trapping potential • : parameters for density- and spin-dependent interactions, respectively. • : Landé hyperfine g-factor • : spin operator (Fx, Fy, Fz)

  5. Dimensionless GP equation • We employ dimensionless units in which the energy, length, and time scales are measured by , and , respectively. • Resulting dimensionless GP equation reads • We look for the numerical solution of the dimensionless GP equation.

  6. GP simulation in two-dimension • The initial Skyrmion configuration is taken from the d-vector

  7. Without magnetic field • Real time solution of GP equation (fixed boundary condition)

  8. Under uniform magnetic field along the z-direction • Real time solution of GP equation (fixed boundary condition)

  9. GP equation in one-dimension • The initial rotational configuration is taken from the d-vector which realized a rapid rotation of the vector over the length R from the origin.

  10. Without magnetic field • Real time solution of GP equation (fixed boundary condition)

  11. Under magnetic field gradient • Real time solution of GP equation (fixed boundary condition)

  12. Sustainable dynamics within the AFM manifold • Special type of state that can still maintain the new dynamics entirely within the AFM manifold. n=1: n=2: n=4:

  13. Sustainable dynamics within the AFM manifold • Real time solution of GP equation (periodic boundary condition)

  14. Conclusion • Numerical solution of GP equation proves that dynamics of spin-1 BEC cannot be supported within AFM manifold (or FM manifold). • (FM; t=0)  (FM+AFM, t>0) • (AFM; t=0)  (AFM+FM, t>0) • Dynamics of special state can sustain the sub-manifold.

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