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Motivated by recent experiments carried out by Spielman’s group at NIST, we study the vortex formation in a rotating Bose–Einstein condensate in synthetic magnetic field confined in a harmonic potential combined with an optical lattice. We obtain numerical solutions of the two-dimensional Gross–Pitaevskii equation and compare the vortex formation by synthetic magnetic field method with those by rotating frame method. We conclude that a large angular momentum indeed can be created in the presence of the optical lattice. However, it is still more difficult to rotate the condensate by the synthetic magnetic field than by the rotating frame even if the optical lattice is added, and the chemical potential and energy remain almost unchanged by increasing rotational frequency.
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