In this paper, the critical rotation rate for vortex nucleation in ultracold rotating boson atoms in 2D deep optical lattices is calculated. We suggest a semiclassical approach to calculate the critical rotation frequency at finite temperature through extension of Stringari threshold formula. The critical rotation frequency is parametrized in terms of the thermodynamic potential. Depending on the semiclassical approximation, the calculated thermodynamic potential enabled us to investigate the finite size and interatomic interaction effects. The calculated results show that the critical rotation rate, as a function of stirring frequency, shows a peak, while the critical rotation rate as a function of the normalized temperature decreases monotonically with the increase in the temperature. The critical rotation rate depends on the interatomic interaction, atoms number and optical potential depth. The obtained results provide useful theoretical foundation for rotating condensate boson in optical lattice.

中文翻译：

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在有限温度下困在二维深光学晶格中的超冷旋转玻色子原子中涡旋成核的临界旋转速率

在本文中，计算了二维深光学晶格中超冷旋转玻色子原子涡旋成核的临界旋转速率。我们建议通过扩展 Stringari 阈值公式来计算有限温度下的临界旋转频率的半经典方法。临界旋转频率根据热力学势进行参数化。根据半经典近似，计算出的热力学势使我们能够研究有限尺寸和原子间相互作用效应。计算结果表明，作为搅拌频率的函数的临界转速显示出峰值，而作为归一化温度的函数的临界转速随着温度的升高而单调降低。临界旋转速率取决于原子间相互作用、原子数和光势深度。所得结果为在光学晶格中旋转凝聚玻色子提供了有用的理论基础。