Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T08:23:18.392Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE GROUND STATE OF SPIN-1 BOSE–EINSTEIN CONDENSATES WITH AN EXTERNAL IOFFE–PITCHARD MAGNETIC FIELD

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  28 May 2012

WEI LUO ,
ZHONGXUE LÜ  and
ZUHAN LIU
WEI LUO
Affiliation:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, PR China
ZHONGXUE LÜ*
Affiliation:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, PR China (email: [email protected])
ZUHAN LIU
Affiliation:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, PR China
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we prove the existence of the ground state for the spinor Bose–Einstein condensates with an external Ioffe–Pitchard magnetic field in the one-dimensional case. We also characterise the ground states of spin-1 Bose–Einstein condensates with an external Ioffe–Pitchard magnetic field; that is, for ferromagnetic systems, we show that, under some condition, searching for the ground state of ferromagnetic spin-1 Bose–Einstein condensates with an external Ioffe–Pitchard magnetic field can be reduced to a ‘one-component’ minimisation problem.

Keywords

ground statesspin-1 Bose–Einstein condensatethe external Ioffe–Pitchard magnetic field

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35B45: A priori estimates
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 356 - 369
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

Research is supported by the Natural Science Foundation of China (No. 10771181; 11071206), NSF of Jiangsu Province (No. BK2010172), the Postgraduate Innovation Project of Jiangsu Province (No. CXZZ11-0901) and Foundation of Xuzhou Normal University (No. 2011YLA003).

References

[1]Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. and Cornell, E. A., ‘Observation of Bose–Einstein condensation in a dilute atomic vapor’, Science 269 (1995), 198–201.CrossRefGoogle Scholar
[2]Bao, W. and Lim, F. Y., ‘Computing ground states of spin-1 Bose–Einstein condensates by the normalized gradient flow’, SIAM J. Sci. Comput. 30 (2008), 1925–1948.CrossRefGoogle Scholar
[3]Bao, W. and Lim, F. Y., ‘Numerical methods for computing the ground state of spin-1 Bose–Einstein condensates in uniform magnetic field’, Phys. Rev. E (3) 78 (2008), article 066704, 11 pages.Google Scholar
[4]Bradley, C. C., Sackett, C. A., Tollett, J. J. and Hulet, R. G., ‘Evidence of Bose–Einstein condensation in an atomic gas with attractive interaction’, Phys. Rev. Lett. 75 (1995), 1687–1690.CrossRefGoogle Scholar
[5]Bulgakov, E. N. and Sadreev, A. F., ‘Vortex phase diagram of F=1 spinor Bose–Einstein condensates’, Phys. Rev. Lett. 90 (2003), 200401–200404.CrossRefGoogle ScholarPubMed
[6]Cao, D., Shern, I.-L. and Wei, J., ‘On ground state of spinor Bose–Einstein condensates’, NoDEA Nonlinear Differential Equations Appl. 18 (2011), 427–445.CrossRefGoogle Scholar
[7]Chang, M., Qin, Q., Zhang, W., You, L. and Chapman, M. S., ‘Coherent spinor dynamics in a spin-1 Bose condensate’, Nature Phys. 1 (2005), 111–116.CrossRefGoogle Scholar
[8]Davis, K. B., Mewes, M.-O., Andrews, M. R., Vam Druten, N. J., Durfee, D. S., Kurn, D. M. and Ketterle, W., ‘Bose–Einstein condensation in a gas of sodium atoms’, Phys. Rev. Lett. 75 (1995), 3969–3973.CrossRefGoogle Scholar
[9]Gross, E. P., ‘Structure of a quantized vortex in boson systems’, Nuovo Cimento X. Ser. 20 (1961), 454–477.CrossRefGoogle Scholar
[10]Ho, T. L. and Shenoy, V. B., ‘Binary mixtures of Bose condensates of alkali atoms’, Phys. Rev. Lett. 77 (1996), 3276–3279.CrossRefGoogle ScholarPubMed
[11]Isoshima, T., Machida, K. and Ohmi, T., ‘Spin-domain formation in spinor Bose–Einstein condensation’, Phys. Rev. A (3) 60 (1999), 4857–4863.CrossRefGoogle Scholar
[12]Lin, L. and Shern, I.-L., ‘Characterization of the ground states of spin-1 Bose–Einstein condensates’, arXiv:1102.0832v2, 2011.Google Scholar
[13]Miesner, H. J., Stamper-Kurn, D. M., Stenger, J., Inouye, S., Chikkatur, A. P. and Ketterle, W., ‘Observation of metatable states in spinor Bose–Einstein condensates’, Phys. Rev. Lett. 82 (1999), 2228–2231.CrossRefGoogle Scholar
[14]Ohmi, T. and Machida, K., ‘Bose–Einstein condensation with internal degrees of free- dom in alkali atom gases’, J. Phys. Soc. Japan 67 (1998), 1822–1825.CrossRefGoogle Scholar
[15]Pitaevskii, L. P., ‘Vortex lines in an imperfect Bose gas’, Soviet Phys. JETP 13 (1961), 451–454.Google Scholar
[16]Pitaevskii, L. P. and Stringari, S., Bose–Einstein Condensation (Clarendon Press, Oxford, 2003).Google Scholar
[17]Stenger, J., Inouye, S., Stamper-Kurn, D. M., Miesner, H. J., Chikkatur, A. P. and Ketterle, W., ‘Spin domians in ground-states Bose–Einstein condensates’, Nature London 396 (1998), 345–348.CrossRefGoogle Scholar