论文标题
激光驱动的量子粒子动力学的直接最佳控制方法
Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics
论文作者
论文摘要
最佳控制理论通常被公式为间接方法，需要解决两点边界值问题的解决方案。实际上，该解决方案是通过量子波袋的迭代向后和向后传播获得的。在这里，我们提出直接最佳控制作为强大而灵活的替代方案。它基于导致非线性优化问题的动态方程的离散化。该方法是针对Bistable电位的激光驱动波袋动力学的情况进行说明的。通过单个高斯函数进行参数化，并针对控制间隔的各种粒子质量和长度进行了场的优化。在全量子传播中使用优化的场仍然可以在大多数考虑的情况下产生合理的控制收率。对偏差的分析会导致必须满足的条件，以使半经典的单高斯近似具有对场优化的有意义。
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.
