arXiv quant-ph/06070482006-07-06quant-phnlin.CD

光晶格中原子的非线性相干动力学

Nonlinear coherent dynamics of an atom in an optical lattice

V. Yu. Argonov, S. V. Prants

发表信息：: V.Yu. Argonov and S.V. Prants. Nonlinear coherent dynamics of an atom in an optical lattice. Journal of Russian Laser Research. V.27 N4 (2006) 360-378.

摘要：

本文考虑了一个简单的二能级单原子与单模驻波激光场的无耗相互作用模型，该模型产生了一维光晶格。原子的内部动力学由激光场控制，激光场被视为具有大量光子的经典场。质心经典原子运动受光学势和原子内部自由度的控制。由此产生的Hamilton-薛定谔方程的运动是一个五维的非线性动力系统的两个运动积分。本文的主要重点是混沌原子运动，可以严格量化的最大李雅普诺夫指数正值。结果表明，原子根据其总能量的大小，既可以在光势阱中作混沌振荡，也可以作动量弱混沌振荡的弹道飞行，还可以在光晶格中以混沌方式改变运动方向的漂移.在混沌状态下，原子的运动具有分形性质。我们发现了一个可视化复杂原子运动的有用工具--将三维相空间中的原子轨道映射到原子内部变量和动量平面上的庞加莱映射。我们发现了典型的非双曲哈密顿系统的共同特征--嵌入随机海中的不同尺寸的共振岛链、随机层、分叉等，发现并数值证明了原子轨道与规则岛边界的粘连现象，这对光晶格中的原子输运有很大的影响.

英文摘要：

We consider a simple model of lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. Internal dynamics of the atom is governed by the laser field which is treated to be classical with a large number of photons. Center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degree of freedom. The resulting Hamilton-Schrödinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion. The main focus of the paper is chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential or fly ballistically with weak chaotic oscillations of its momentum or wander in the optical lattice changing the direction of motion in a chaotic way. In the regime of chaotic wandering atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion -- Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. We find common features with typical non-hyperbolic Hamiltonian systems -- chains of resonant islands of different sizes embedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of sticking of atomic trajectories to boundaries of regular islands, that should have a great influence to atomic transport in optical lattices, is found and demonstrated numerically.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文