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arXiv quant-ph/0701038quant-ph
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光晶格中原子的混沌输运理论

Theory of chaotic atomic transport in an optical lattice

V. Yu. Argonov, S. V. Prants

备注：
14 pages, 8 figures
发表信息：
V.Yu. Argonov and S.V. Prants. Theory of chaotic atomic transport in an optical lattice. Phys. Rev. A. V.75 (2007) art. no. 063428.
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摘要：

本文发展了一维非耗散光晶格中混沌原子输运的半经典理论。使用的布洛赫和平移原子变量的运动的基本方程，我们推导出一个随机映射的同步分量的原子的偶极矩，决定了质心运动。我们发现原子和晶格参数之间的分析关系，原子通常在飞行通过晶格和被困在光势阱之间交替。我们使用随机地图来推导飞行和捕获事件的概率密度函数（PDF）的公式。混沌原子输运的统计特性强烈依赖于原子参数和晶格参数之间的关系。我们发现，有一个很好的定量协议之间的分析PDF和那些计算的随机地图和基本方程的运动参数的不同范围。典型的飞行和捕获PDF显示为具有幂律"头部“和指数"尾部”的宽分布，斜率为-1.5。PDF的幂律和指数部分的长度取决于参数的值，并且可以连续变化。我们发现的分析条件下，确定性的原子输运具有分形特性，并解释了层次结构的动力学分形。

英文摘要：

A semiclassical theory of chaotic atomic transport in a one-dimensional nondissipative optical lattice is developed. Using the basic equations of motion for the Bloch and translational atomic variables, we derive a stochastic map for the synchronized component of the atomic dipole moment that determines the center-of-mass motion. We find the analytical relations between the atomic and lattice parameters under which atoms typically alternate between flying through the lattice and being trapped in the wells of the optical potential. We use the stochastic map to derive formulas for the probability density functions (PDFs) for the flight and trapping events. Statistical properties of chaotic atomic transport strongly depend on the relations between the atomic and lattice parameters. We show that there is a good quantitative agreement between the analytical PDFs and those computed with the stochastic map and the basic equations of motion for different ranges of the parameters. Typical flight and trapping PDFs are shown to be broad distributions with power law ``heads'' with the slope -1.5 and exponential ``tails''. The lengths of the power law and exponential parts of the PDFs depend on the values of the parameters and can be varied continuously. We find analytical conditions, under which deterministic atomic transport has fractal properties, and explain a hierarchical structure of the dynamical fractals.

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