Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates

1. FB18 Aug. 24, 2006 Symmetry Breaking in Scalar, Spinor, and Rotating Bose-Einstein condensates Univ. of Electro-Communications, Japan Hiroki Saito Tokyo Institute of Technology, Japan Yuki Kawaguchi Masahito Ueda Univ. of Arizona, Tucson Rina Kanamoto

2. Contents Symmetry breaking in BEC 1. rotation symmetry breaking in attractive BEC 2. clockwise-counterclockwise symmetry breaking in ferromagnetic BEC 3. chiral symmetry breaking in dipolar BEC

3. 1D attractive BEC 1D infinite space bright soliton translation symmetry breaking 1D ring rotation symmetry breaking

4. Critical localization on a ring density excitation energy gN Goldstone mode attractive interaction energy > zero point energy localization RK, HS, and MU, PRA 67 013608 (2003); PRA 68 043619 (2003); PRL 94 090904 (2005); PRA 73 033611 (2006)

5. Single vortex ------ ring geometry axi-symmetric vortex state topological defect ringlike geometry attractive interaction rotation symmetry breaking

6. Symmetry breaking in rotating attractive BEC excitation energy Goldstone mode rotation symmetry breaking split-merge cycle HS and MU, PRL 89 190402 (2002); PRA 69 013604 (2004)

7. Magnetization of spinor BEC Ferromagnetic interaction (e.g. spin-1 87Rb) The initial state is prepared in non-magnetic state. (e.g. mF=0) violation of spin conservation How does magnetization occur in isolated systems? spin texture e.g. domain structure HS and MU, PRA 72, 023610 (2005)

8. ferromagnetic energy energy cost at domain walls > Topological texture formation polar-core vortex spontaneous formation of topological texture degenerate HS, YK, and MU, PRL 96, 065302 (2006)

9. Polar-core vortex formation m=1 component initial state m = 0 + noise clockwise-counterclockwise symmetry breaking

10. Energy of broken symmetry state

11. Recent experiment in Berkeley magnitude of spin direction of spin Sadler et al., cond-mat/0605351

12. Dipolar interaction dipolar interaction long range anisotropic 52Cr dipolar BEC has been realized in Stuttgart. Griesmaier et al., PRL 94 10401 (2005) dipolar magnetic field YK, HS, and MU, PRL 96, 080405 (2006)

13. ferromagnetic spin-1 87Rb BEC Ground state spin texture dipole energy kinetic energy dipole energy kinetic energy << >> x-z plane x-y plane magnetic closure single domain

14. Chiral symmetry breaking dipole energy kinetic energy ~ x-z plane x-y plane Chiral symmetry breaking YK, HS, and MU, to appear in PRL

15. Spontaneous circulation orbital angular momentum dipole interaction / kinetic energy Nonzero circulation by chiral symmetry breaking

16. Summary 1. Rotation symmetry breaking vortex split by attractive interaction 2. Clockwise-counterclockwise symmetry breaking topological spin texture formation 3. Chiral symmetry breaking ground state with dipolar interaction