We study the thermodynamics of ultracold Bose atoms in optical lattices by numerically diagonalizing the mean-field Hamiltonian of the Bose-Hubbard model. This method well describes the behavior of long-range correlations and therefore is valid deep in the superfluid phase. For the homogeneous Bose-Hubbard model, we draw the finite-temperature phase diagram and calculate the superfluid density at unity filling. We evaluate the finite-temperature effects in a recent experiment probing number fluctuation [Phys. Rev. Lett. 96 090401 (2006)], and find that our finite-temperature curves give a better fitting to the experimental data, implying non-negligible temperature effects in this experiment.

中文翻译：

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有限温度对超流体到莫特绝缘体转变过程中超冷原子数波动的影响

我们通过对 Bose-Hubbard 模型的平均场哈密顿量进行数值对角化来研究光学晶格中超冷 Bose 原子的热力学。该方法很好地描述了长程相关的行为，因此在超流体相深处是有效的。对于均质 Bose-Hubbard 模型，我们绘制了有限温度相图并计算了单位填充时的超流体密度。我们在最近的一项探测数字波动的实验中评估了有限温度效应 [Phys. 牧师莱特。96 090401 (2006)]，并发现我们的有限温度曲线更好地拟合了实验数据，这意味着该实验中的温度效应不可忽略。