Abstract
We have calculated the F = 1 ground state of a spinor Bose-Einstein condensate trapped harmonical potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F z = −1 antiferromagnetic condensate are separated in space. Moreover we considered an average local spin \(\left| {\left\langle {\overrightarrow S } \right\rangle } \right|\) to testify to what extend it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.
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References
Achenbach J.D.: 1973. Wave Propagation in Elastic Solids. North-Holland, Amsterdam
Anderson M.H., Ensher J.R., Matthews M.R., Weiman C.E. and Cornell E.A.: 1995. Science, 269, 198
Aronson I.S. and Tsimring L.S.: 2006. Rev. Mod. Phys., 78, 641
Barth M. and Stöckmann H.-J.: 2002. Phys. Rev. E, 65, 066208
Berry M.V.: 1977. J. Phys. A, 10, 2083
Berry M.V.: 1981. In: R. Balian, M. Klaeman,, J.-P. Poirier (eds.): Physics of Defects, Les Houches Lecture Series Session XXXV. North Holland, Amsterdam,
Bialynicki-Birula I., Bialynicka-Birula Z. and Sliwa C.: 2000. Phys. Rev. A, 61, 032110
Bulgakov E.N. and Sadreev A.F.: 2003. Phys. Rev. Lett., 90, 200401
Chakraborty T. and Pietiläinen P.: 1995. The Quantum Hall Effects: Fractional and Integral. Springer, Berlin
Chen Y.F. and Huang K.F.: 2003. Phys. Rev. E, 68, 066207
Chen Y.F., Lu T.H. and Huang K.F.: 2006a. Phys. Rev. Lett., 96, 033901
Chen Y.F., Lu T.H. and Huang K.F.: 2006b. Phys. Rev. Lett., 97, 233903
Courtial J. and O'Holleran K.: 2007. Eur. Phys. J. Special Top., 145, 35
Davis K.B. et al: 1995. Phys. Rev. Lett., 75, 3969
Dennis M.R.: 2003. J. Phys. A: Math. Gen., 36, 6611
Dirac P.A.M.: 1931. Proc. R. Soc. London, Ser. A, 133, 60
Dorrestijn M. et al: 2007. Phys. Rev. Lett., 98, 26102
Dubrovin B.A., Fomenko A.T., Novikov S.P.: 1985. Modern geometry-methods and applications. Part II, The geometry and topology of manifolds. Graduate Texts in Mathematics, vol. 104, Springer, New York,
Ebeling K.J.: 1984. Statistical Properties of Random Wave Fields in Physical Acoustics: Principles and Methods. Academic, New York
Flossmann F., O'Holleran K., Dennis M.D. and Padgett M.J.: 2008. Phys. Rev. Lett., 100, 203902
Freund I. and Kessler D.A.: 1996. Opt. Commun., 124, 321
Hirschfelder J.O, Christoph A.C. and Palke W.E.: 1974a. J. Chem. Phys., 61, 5435
Hirschfelder J.O, Goebel C.J. and Bruch L.W.: 1974b. J. Chem. Phys., 61, 5456
Ho T.-L.: 1998. Phys. Rev. Lett., 81, 742
Ho T.-L. and Shenoy V.B.: 1996. Phys. Rev. Lett., 77, 2595
Isoshima T. and Machida K.: 2002. Phys. Rev. A, 66, 023602
Isoshima T. and Yip S.: 2006. J. Phys. Soc. Jpn., 75, 074605
Isoshima T., Nakahara M., Ohmi T. and Machida K.: 2000. Phys. Rev. A, 61, 063610
Khawaja U.A. and Stoof H.T.C.: 2001. Phys. Rev. A, 64, 043612
Kim Y.-H., Barth M., Kuhl U. and Stöckmann H.-J.: 2003. Progr. Theor. Phys. Suppl., 150, 105
Klausen N.N. et al: 2001. Phys. Rev. A, 64, 053602
Landau L.D., Lifshitz E.M.: 1959. Theory of Elasticity. Pergamon, Oxford,
Landau L.D. and Lifshitz E.M.: 1975. Quantum Mechanics. Non-Relativistic Theory. Perga-mon, New York
Leanhardt A.E.: 2003. Microtraps and Waveguides for Bose-Einstein Condensates. PhD Thesis, Massachusetts Institute of Technology
Leanhardt A.E., Shin Y., Kielpinski D., Pritchard D.E. and Ketterle W.: 2003. Phys. Rev. Lett., 90, 140403
Liu F. and Mazenko G.F.: 1992. Phys. Rev. B, 46, 5963
Madelung E.: 1926. Z. Phys., 40, 322
Maksimov D.N. and Sadreev A.F.: 2007. JETP Lett., 86, 670
Maksimov D.N. and Sadreev A.F.: 2008. Phys. Rev. E, 77, 056204
Martikainen J.-P., Collin A. and Suominen K.-A.: 2002. Phys. Rev. A, 66, 043613
Marzlin K.-P., Zhang W. and Sanders B.C.: 2000. Phys. Rev. A, 62, 013602
Miesner H.-J. et al: 1999. Phys. Rev. Lett., 82, 2228
Mizushima T., Machida K. and Kita T.: 2002a. Phys. Rev. A, 66, 053610.
Mizushima T., Machida K. and Kita T.: 2002b. Phys. Rev. Lett., 89, 030401
Mizushima T., Kobayashi N. and Machida K.: 2004. Phys. Rev. A, 70, 043613
Mueller E.J.: 2004. Phys. Rev. A, 69, 033606
Nye J.F. and Berry M.V.: 1974. Proc. R. Soc. London, Ser. A, 336, 165
Ohmi T. and Machida K.: 1998. J. Phys. Soc. Jpn., 67, 1822
Petrich W., Anderson M.H., Ensher J.R. and Cornell E.A.: 1995. Phys. Rev. Lett., 74, 3352
Saarikoski H., Harju A., Puska M.J. and Nieminen R.M.: 2004. Phys. Rev. Lett., 93, 116802
Saint-James D. and Sarma G.: 1969. Type II Superconductivity. Pergamon Press, Oxford
Shvartsman N. and Freund I.: 1994. Phys. Rev. Lett., 72, 1008
Soskin M.S. et al: 1997. Phys. Rev. A, 56, 4064
Stamper-Kurn D.M. et al: 1998. Phys. Rev. Lett., 80, 2027
Stenger J. et al: 1998. Nature (London), 369, 345
Thomas B. and Squires A.M.: 1998. Phys. Rev. Lett., 81, 574
Waller M.D.: 1952. Proc. R. Soc. London, Ser. A, 211, 265
Waterhouse R.V.: 1985. J. Acoust. Soc. Am., 76, 758
Waterhouse R.V.: 1987. J. Acoust. Soc. Am., 82, 1782
Whewell W.: 1833. Phil. Trans. Roy. Soc. London, 123, 147
Yip S.-K.: 1999. Phys. Rev. Lett., 83, 4677
Zhang P., Jen H.H., Sun C.P. and You L.: 2007. Phys. Rev. Lett., 98, 030403
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Sadreev, A.F. (2009). Vortices in the Ground State of Spinor Bose-Einstein Condensates. In: Casati, G., Matrasulov, D. (eds) Complex Phenomena in Nanoscale Systems. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3120-4_10
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DOI: https://doi.org/10.1007/978-90-481-3120-4_10
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