Abstract

Coherent dynamics of cold atoms in a 2D optical lattice with interfering laser beams is studied with account for internal and external degrees of freedom of an atom. A system of differential equations for coupled degrees of freedom obtained in the semiclassical approximation has regular and chaotic solutions depending on the atomic-field detuning from resonance. The Hamilton chaos is manifested in the form of chaotic Rabi oscillations and random walks of cold atoms in the lattice for relatively small resonance detunings. It is shown that the deterministic chaos appears as a result of jumps in the value of the electric dipole moment of an atom approaching the nodes of a 2D standing wave. This in turn causes a pseudorandom behavior of momenta of atoms and, as a consequence, their random walks in the absolutely rigid 2D optical lattice without any external modulation of its parameters. It is shown in numerical experiments with 10⁶ atoms that their distributions over the lattice for different resonance detunings differ significantly. This fact can be used for detecting the effect of random walks of cold atoms in a real experiment by the absorption image method.

中文翻译：

---

二维光学晶格中冷原子的混沌行走

摘要

考虑到原子的内部和外部自由度，研究了带有干扰激光束的二维光学晶格中冷原子的相干动力学。在半经典近似中获得的耦合自由度的微分方程组具有正则解和混沌解，这取决于原子场因共振而失谐。汉密尔顿混沌表现为混沌的拉比振荡和相对较小的共振失谐在晶格中的冷原子随机游走的形式。结果表明，确定性混沌的出现是原子接近二维驻波节点的电偶极矩值跃变的结果。反过来，这会导致原子动量的伪随机行为，因此，它们的随机行走在绝对刚性的2D光学晶格中，而无需对其参数进行任何外部调制。在10个数值实验中显示^有6个原子，它们在不同共振失谐下在晶格上的分布差异很大。该事实可用于通过吸收图像法在实际实验中检测冷原子随机游动的影响。