Experimental study of quantum chaos using atom optics technique

该项目旨在利用电磁操纵原子来解决量子混沌问题。以下是我们为实现这一目标而进行的研究成果。我们预测，当磁场周期性调制时，被困在磁势中的原子的经典运动将变得混沌。将Rb原子激光冷却至10 μ K，然后在录像带原子芯片上进行参数化加热。基于牛顿运动方程的数值模拟很好地再现了观测到的光谱，表明原子的行为与经典粒子一样。我们用数值方法证明了在不改变原子云内能的情况下冷却或加热原子云。这些研究是与伦敦帝国理工学院冷物质研究中心合作进行的。当光强周期性调制时，空芯光纤中光引导原子的横向运动变得混沌。对于入射原子的激光冷却，我们稳定了新引入的二极管激光器的频率。磁光阱的建造正在进行中。我们还开发了一种利用电磁感应透明的新型稳频方法。两种类型的光学陷阱，都是使用反向传播激光束，开发了微尺寸的粒子。首次证明了六边形冰晶的激光俘获。在CO_2激光阱中，气流抵消了重力作用，延长了阱时间。基于射击法，提出了一种搜索非可积系统周期轨道的新算法。用各向异性开普勒问题和电磁场中的氢原子验证了其可行性。显著节省了CPU时间。

The project aims to solve the problem of quantum chaos using electromagnetically manipulated atoms. Summarized below are the outcomes of our research carried out toward this goal.1. We predicted that classical motion of atoms trapped in a magnetic potential becomes chaotic when the magnetic field is periodically modulated. Rb atoms were once laser-cooled to 10 μ K, then parametrically heated on the video-tape atom chip. The observed spectrum is well reproduced by numerical simulations based on Newton's equations of motion, showing that atoms behave as classical particles. We numerically demonstrated cooling or heating of the atom cloud without changing their internal energy. These researches were carried out in cooperation with Center for Cold Matter, Imperial College London.2. The transverse motion of atoms optically guided in a hollow-core fiber becomes chaotic when the light intensity is periodically modulated. For laser-cooling of the incident atoms, we stabilized the frequency of the newly introduced diode laser. Construction of a magneto-optical trap is now in progress. We have also developed a novel method of frequency stabilization that uses electromagnetically induced transparency.3. Two types of optical traps, both of which use counter propagating laser beams, were developed for micro-sized particles. Laser trapping of hexagonal ice crystals was demonstrated for the first time. In the CO_2 laser trap, air flow counteracts gravity and prolongs the trap time.4. Based on the shooting method, we developed a novel algorithm to search periodic orbits of a non-integrable system. Its feasibility was tested on the anisotropic Kepler problem and a hydrogen atom in electromagnetic fields. CPU time was remarkably saved.