脉冲式棘齿势场作用下囚禁离子的规则与混沌运动

考虑赝势近似下囚禁于Paul阱中的单离子与由脉冲式双激光驻波构成的棘齿势场的相互作用.应用积分方程方法得到系统的经典运动精确解，通过数值方法作出相空间轨道并计算由平均速度定义的流，结合分析与数值结果研究囚禁离子的规则与混沌运动特性.与单驻波型激光脉冲情形相比，发现两个重要的棘齿效应：一是脉冲式棘齿势场的作用导致参数空间混沌区域的改变，从而适当调节第二驻波参数，可使离子的规则运动变为混沌运动，或者混沌运动变为规则运动；二是通过分析平均流随激光参数的变化，发现棘齿势场的介入能使囚禁离子作平均意义下的单向输运，随着势场强度增加到混沌区域，流的强度明显减小并改变方向，系统进入混沌运动. 关键词： 脉冲式棘齿势 囚禁离子 混沌 输运

Regular and chaotic motions of a single trapped ion interacting with a flashing ratchet potential

Under the pseudopotential approximation, for a single Paul trapped ion which interacts with a flashing ratchet potential formed by two laser standing waves, we apply the method of integral-equation to construct the exact solution of the classical equation, and use the numerical technique to plot the orbits in phase space and calculate the current defined by the average velocity. By combining the analytical results with numerical ones,we investigate the regular and chaotic motions of the system. Compared to the case of the flashing lattice potential, two important ratchet effects are found here: First, the flashing ratchet potential changes the chaotic region in the parameter space such that we can make the regular motion of ion chaotic or vice versa by adjusting the parameters of the second laser. Secondly, by analyzing the evolutions of the average current versus the laser parameters, we find that the presence of the flashing ratchet potential can lead the trapped ion to be transported in averagy along a single direction. When the potential strength is increased to the chaotic region, the current decreases evidently and its direction varies, indicating the onset of chaotic motion.