Efficient continuation methods for spin-1 Bose–Einstein condensates in a magnetic field

References

• W. Bao and Y. Cai, Ground states and dynamics of spin-orbit-coupled Bose–Einstein condensates, SIAM J. Appl. Math. 75 (2015), pp. 492–517. doi: 10.1137/140979241
   Web of Science ®Google Scholar
• W. Bao, I.-L. Chern, and Y. Zhang, Efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates based on their characterizations, J. Comput. Phys. 253 (2013), pp. 189–208. doi: 10.1016/j.jcp.2013.06.036
   Web of Science ®Google Scholar
• W. Bao and F.Y. Lim, Computing ground states of spin-1 Bose–Einstein condensates by the normalized gradient flow, SIAM J. Sci. Comput. 30 (2008), pp. 1925–1948. doi: 10.1137/070698488
   Web of Science ®Google Scholar
• W. Bao and H. Wang, A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose–Einstein condensates, SIAM J. Numer. Anal. 45 (2007), pp. 2177–2200. doi: 10.1137/070681624
   Web of Science ®Google Scholar
• W. Bao and Y. Zhang, Dynamical laws of the coupled Gross–Pitaevskii equations for spin-1 Bose–Einstein condensates, Methods Appl. Anal. 17 (2010), pp. 49–80.
   Google Scholar
• M.D. Barrett, J.A. Sauer, and M.S. Chapman, All-optical formation of an atomic Bose–Einstein condensate, Phys. Rev. Lett. 87 (2001), pp. 010404:1–4. doi: 10.1103/PhysRevLett.87.010404
   Web of Science ®Google Scholar
• D. Cao, I.-L. Chern, and J.-C. Wei, On ground state of spinor Bose–Einstein condensates, Nonlinear Differ. Equ. Appl. (NoDEA) 18 (2011), pp. 427–445. doi: 10.1007/s00030-011-0102-9
   Web of Science ®Google Scholar
• J.-H. Chen, I.-L. Chern, and W. Wang, Exploring ground states and excited states of spin-1 Bose–Einstein condensates by continuation methods, J. Comput. Phys. 230 (2011), pp. 2222–2236. doi: 10.1016/j.jcp.2010.11.048
   Web of Science ®Google Scholar
• H.-S. Chen, S.-L. Chang, and C.-S. Chien, Spectral collocation methods using sine functions for a rotating Bose–Einstein condensation in optical lattices, J. Comput. Phys. 231 (2012), pp. 1553–1569. doi: 10.1016/j.jcp.2011.10.030
   Web of Science ®Google Scholar
• J.-H. Chen, I.-L. Chern, and W. Wang, A complete study of the ground state phase diagrams of spin-1 Bose–Einstein condensates in a magnetic field via continuation methods, J. Sci. Comput. 64 (2014), pp. 35–54. doi: 10.1007/s10915-014-9924-z
   Web of Science ®Google Scholar
• A. Görlitz, T.L. Gustavson, A.E. Leanhardt, R. Löw, A.P. Chikkatur, S. Gupta, S. Inouye, D.E. Pritchard, and W. Ketterle, Sodium Bose–Einstein condensates in the F=2 state in a large-volume optical trap, Phys. Rev. Lett. 90 (2003), pp. 090401:1–4. doi: 10.1103/PhysRevLett.90.090401
   Web of Science ®Google Scholar
• T.-L. Ho, Spinor Bose condensates in optical traps, Phys. Rev. Lett. 81 (1998), pp. 742–745. doi: 10.1103/PhysRevLett.81.742
   Web of Science ®Google Scholar
• G. Iooss and M. Adelmeyer, Topics in Bifurcation Theory and Applications, 2nd ed., World Scientific, Singapore, 1998.
   Google Scholar
• T. Isoshima and S. Yip, Effect of quadratic Zeeman energy on the vortex of spinor Bose–Einstein condensates, J. Phys. Soc. Japan 75 (2006), pp. 074605:1–6. doi: 10.1143/JPSJ.75.074605
   Google Scholar
• T. Isoshima, K. Machida, and T. Ohmi, Spin-domain formation in spinor Bose–Einstein condensation, Phys. Rev. A 60 (1999), pp. 4857–4863. doi: 10.1103/PhysRevA.60.4857
   Web of Science ®Google Scholar
• D. Jacob, L. Shao, V. Corre, T. Zibold, L. De Sarlo, E. Mimoun, J. Dalibard, and F. Gerbier, Phase diagram of spin-1 antiferromagnetic Bose–Einstein condensates, Phys. Rev. A 86 (2012), pp. 061601:1–5. doi: 10.1103/PhysRevA.86.061601
   Google Scholar
• C.K. Law, H. Pu, and N.P. Bigelow, Quantum spins mixing in spinor Bose–Einstein condensates, Phys. Rev. Lett. 81 (1998), pp. 5257–5261. doi: 10.1103/PhysRevLett.81.5257
   Web of Science ®Google Scholar
• F.Y. Lim and W. Bao, Numerical methods for computing the ground state of spin-1 Bose–Einstein condensates in a uniform magnetic field, Phys. Rev. E 78 (2008), pp. 066704:1–11. doi: 10.1103/PhysRevE.78.066704
   Web of Science ®Google Scholar
• L. Lin and I.-L. Chern, A kinetic energy reduction technique and characterizations of the ground states of spin-1 Bose–Einstein condensates, Discret. Contin. Dyn. Syst. Ser. B 19 (2014), pp. 1119–1128. doi: 10.3934/dcdsb.2014.19.3105
   Web of Science ®Google Scholar
• M. Matuszewski, T.J. Alexander, and Y.S. Kivshar, Excited spin states and phase separation in spinor Bose–Einstein condensates, Phys. Rev. A 80 (2009), pp. 023602:1–9. doi: 10.1103/PhysRevA.80.023602
   Web of Science ®Google Scholar
• T. Ohmi and K. Machida, Bose–Einstein condensation with internal degrees of freedom in Alkali atom gases, J. Phys. Soc. Japan 67 (1998), pp. 1822–1825. doi: 10.1143/JPSJ.67.1822
   Google Scholar
• L.E. Sadler, J.M. Higbie, S.R. Leslie, M. Vengalattore, and D.M. Stamper-Kurn, Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate, Nature 443 (2006), pp. 312–315. doi: 10.1038/nature05094
   PubMed Web of Science ®Google Scholar
• H. Saito and M. Ueda, Spontaneous magnetization and structure formation in a spin-1 ferromagnetic Bose–Einstein condensate, Phys. Rev. A 72 (2005), pp. 023610:1–7.
   Web of Science ®Google Scholar
• J. Stenger, S. Inouye, D.M. Stamper-Kurn, H.-J. Miesner, A.P. Chikkatur, and W. Ketterle, Spin domains in ground state spinor Bose–Einstein condensates, Nature 396 (1998), pp. 345–348. doi: 10.1038/24567
   Web of Science ®Google Scholar
• Y.-S. Wang and C.-S. Chien, A two-parameter continuation method for computing numerical solutions of spin-1 Bose–Einstein condensates, J. Comput. Phys. 256 (2014), pp. 198–213. doi: 10.1016/j.jcp.2013.08.056
   Web of Science ®Google Scholar
• W. Zhang, S. Yi, and L. You, Mean field ground state of a spin-1 condensate in a magnetic field, New J. Phys. 5 (2003), pp. 77–89. doi: 10.1088/1367-2630/5/1/377
   Web of Science ®Google Scholar