冷原子在光晶格中扩散的分数阶Lévy动力学理论
Theory of fractional-Lévy kinetics for cold atoms diffusing in optical lattices
摘要：
最近，超冷~（87）Rb原子在光晶格中的反常超扩散被观测到，并具有Lévy型的厚尾空间分布。发现反常指数依赖于光学势的深度。在西西弗斯冷却的半经典理论的框架内，我们发现，随着光学位深的降低，动力学有三个不同的阶段：正常扩散;莱维扩散; x ~ t^3/2标度，后者与奥布霍夫（1959）的湍流模型有关。这个过程可以用一个Lévy walk来表述，在远足的长度和持续时间之间有很强的相关性。我们导出了描述原子云的分数阶扩散方程和相应的反常扩散系数。
英文摘要：
Recently, anomalous superdiffusion of ultra cold 87Rb atoms in an optical lattice has been observed along with a fat-tailed, Lévy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical potential. We find, within the framework of the semiclassical theory of Sisyphus cooling, three distinct phases of the dynamics, as the optical potential depth is lowered: normal diffusion; Lévy diffusion; and x ~ t^3/2 scaling, the latter related to Obukhov's model (1959) of turbulence. The process can be formulated as a Lévy walk, with strong correlations between the length and duration of the excursions. We derive a fractional diffusion equation describing the atomic cloud, and the corresponding anomalous diffusion coefficient.
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