| Quantized vortices are one of the basic phenomena in superfluid and superconductor. For neutral atoms gaseous, vortices can be usually created by the rotating frame method. Recently, vortices were observed in a synthetic magnetic field experiment, and one expects that it can effectively add large angular momentum. In this thesis, we study the formation of vortices in a Bose-Einstein condensate in a synthetic magnetic field by numerically solving the Gross-Pitaevskii (GP) equation.For the condensates confined within a harmonic potential, we find that the the rotating efficiency in synthetic magnetic field is lower than that in rotating frame case at the same rotational frequency, which is different from people’s expectation. In the rotating frame, the effective trapping potential is weakened with the rotational frequency. The weaker is the confinement, the easier is the formation of vortices. Nevertheless, in the synthetic magnetic field case, the trapping potential is independent of the rotational frequency. Increasing the contact interaction between atoms is constructive to create more vortices, even the Abrikosov-lattice-like structures can be formed. Moreover, the validity of the Feynman rule is verified.Second, we investigate the vortex formation process subject to a harmonic potential and an optical lattice. We find that the introduction of the optical lattice increases the vortex number, but the synthetic magnetic field still cannot add as large angular momentum as the rotating frame. The calculation results show that the chemical potential and energy remain almost unchanged by increasing rotational frequency.At last, we consider the effect of dipolar interaction on the vortex formation process. Numerical results indicate that the vortex formation process manifests itself as the directional dependence of the polarization angle. With increasing rotational frequency, the vortex number and the vortex row number are much smaller than those calculated for the rotating frame. |
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