In the present paper, we calculate the superfluid fraction and the critical synthetic magnetic field for vortices nucleation of synthetically charged condensate boson gases trapped in 2D deep optical lattice. The superfluid fraction is parametrized in terms of the moment of inertia, while the critical synthetic field is defined as the ratio between the magnetic free energy and the thermal average of the angular momentum. These calculations are realized in the semiclassical approximation. The effects of finite size effect, the interatomic interaction and the synthetic magnetic field strength are investigated. The extracted results show crucial dependence of the vortical configuration on the above mentioned parameters.

在本文中，我们计算了捕获在二维深光学晶格中的带电带电凝结玻色子气体的涡旋形核的超流体分数和临界合成磁场。根据惯性矩对超流体分数进行参数化，而关键合成场定义为磁自由能与角动量热均值之比。这些计算以半经典近似实现。研究了有限尺寸效应，原子间相互作用和合成磁场强度的影响。提取的结果显示出旋涡构型对上述参数的关键依赖性。