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A Complete Study of the Ground State Phase Diagrams of Spin-1 Bose–Einstein Condensates in a Magnetic Field Via Continuation Methods

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Abstract

We present a complete investigation of the ground state patterns and phase diagrams of the spin-1 Bose–Einstein condensates (BEC) confined in a harmonic or box potential under the influence of a homogeneous magnetic field. A pseudo-arclength continuation method with parameter switching technique is developed to study the BEC systems numerically. The continuation process is performed on the parameter space consisting of the spin–independent interaction, spin–exchange interaction and the quadratic Zeeman (QZ) energy parameters. In the first stage of the parameter switching process, we fix the QZ energy term to be zero and vary the interaction parameters from zero to the desired physical values. Next, we fix the interaction parameters and vary the QZ energy parameter in both positive and negative regions. Two types of phase transitions are found, as we vary the QZ parameter. The first type is a transition from a two-component state to a three-component (3C) state. The second type is a symmetry breaking in the 3C state. Then, a phase separation of the spin components follows. In the semi-classical regime, we find that these two phase transition curves are gradually merged.

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Acknowledgments

The authors are grateful to the anonymous referees for their useful comments and suggestions. This work is partially supported by the National Center for Theoretical Sciences and the National Science Council of the Republic of China under contract numbers: NSC 102-2115-M-134-004 (Chen), NSC 102-2115-M-009-013 (Chern), and NSC 100-2628-M-002-011-MY4 (Wang).

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Authors and Affiliations

  1. Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu, 300, Taiwan

    Jen-Hao Chen

  2. Department of Mathematics, National Central University, Jhongli, 32001, Taiwan

    I-Liang Chern

  3. Institute of Applied Mathematical Sciences, National Taiwan University, Taipei, 106, Taiwan

    I-Liang Chern & Weichung Wang

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  1. Jen-Hao Chen
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  2. I-Liang Chern
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  3. Weichung Wang
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Correspondence to I-Liang Chern.

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Chen, JH., Chern, IL. & Wang, W. 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, 35–54 (2015). https://doi.org/10.1007/s10915-014-9924-z

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  • DOI: https://doi.org/10.1007/s10915-014-9924-z

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