利用移动势阱优化量子粒子输运
Optimization of conveyance of quantum particles by moving potential well
AI总结：
本文研究移动势阱输运量子粒子的存活概率，分析加速与减速过程中非解析速度变化和退相干导致的概率下降，并提出利用束缚态存活概率差异选择基态粒子的方法。
摘要：
利用束缚势阱对粒子位置进行量子力学控制，是操纵量子粒子的一个重要问题。我们研究了粒子被束缚在势阱中成功输运的概率，即在给定长度和给定固定时间内携带粒子过程中的存活概率。对于实际的输运运动，我们需要先加速粒子使其运动，然后减速使其在目的地停止。首先，通过直接数值计算、Wentzel-Kramers-Brillouin方法以及共振态方法，详细研究了恒定加速度速率下存活概率的弛豫行为。发现存活概率在长时间内呈现指数衰减，并从本征值问题的角度对此进行了分析。存活概率下降的一个重要来源是起点处速度的非解析变化。当静止粒子开始运动时，静止参考系的基态被重新分配到运动参考系的本征态上，随后运动参考系的各个本征态随时间演化。分布布居的波函数退相干降低了成功输运的概率。一般而言，平滑启动会产生较小的初始扰动，但在固定时间内到达目的地需要在过程中施加较大的加速度，这会导致过程中更大的存活概率下降。考虑到这些相互矛盾的因素，我们研究了具体输运方案中的存活概率。我们观察了输运过程中束缚概率和布居分布的时间演化。在势阱具有多个束缚态的情况下，我们提出了一种利用束缚态存活概率差异来选择束缚在基态粒子的方法。
英文摘要：
Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of a particle trapping in a potential well, i.e., survival probability in the process carrying of the particle for a given length within a given fixed time. For the actual motion of conveyance, we need to accelerate the particle to move and then decelerate it to stop at the destination. First, the relaxation of the survival probability in a constant acceleration rate is studied in detail by direct numerical calculation, the Wentzel-Kramers-Brillouin method, and a method of the resonance states. The survival probability was found to show an exponential decay in a long time, which is analyzed from a viewpoint of eigenvalue problem. An important source of dropoff comes from a non-analytic change of velocity at the starting point. When the rested particle begins to move, the ground state of the rest frame is redistributed to eigenstates of the moving frame, and then each eigenstate of the moving frame evolves in time. The dephasing of wave functions of the distributed populations reduces the probability of successful conveyance. In general, a smooth start gives a small initial disturbance but requires a large acceleration during the process to reach the destination in the fixed time which causes a larger dropoff in the process. Considering these conflicting facts, we study the survival probability in concrete conveyance schemes. We observe the time evolution of the trapped probability and the population distribution during the conveyance process. In cases that the potential well has several bound states, we propose a method to select the particle trapped at the ground state by making use of the difference of survival probabilities of bound states.
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