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设计整形脉冲场调控分子取向在立体化学反应、强场电离及量子信息处理等领域具有重要的应用价值.然而，传统量子最优控制算法通常在无穷维转动空间中优化分子取向度，且未充分考虑实验设计中脉冲所需满足的约束条件.针对这一问题，本文提出一种多目标多约束量子最优控制算法，用于设计满足脉冲面积和能量约束的脉冲场，以优化超冷分子有限个低位转动态的布居和相位分布，从而得到最大分子取向.研究结果表明，通过调控约束条件，可有效抑制非目标态空间转动态的影响，在目标态空间内获得转动态布居和相位优化的相干叠加态，形成期望的最大分子取向.优化脉冲的时频谱分析结合含时取向度傅里叶变换谱计算表明，获得的最大分子取向主要通过多色脉冲场的爬梯激发实现，且高激发态相干对最大取向度的贡献较小.本文为利用多约束优化算法设计实验可行性脉冲场，通过精准调控有限个转动态产生最大分子取向提供了一种可参考的方法.The design of shaped pulse fields for controlling molecular orientation has significant implications for stereochemical reactions, strong-field ionization, and quantum information processing. Traditional quantum optimal control algorithms typically address molecular orientation in an infinite-dimensional rotational space, yet they often overlook the constraints imposed by experimental limitations. In response, we propose a multi-objective and multi-constraint quantum optimal control algorithm aimed at designing pulse fields that adhere to constraints on pulse area and energy. Specifically, the algorithm enforces a zero pulse area condition to eliminate the static field component and maintains constant pulse energy, ensuring compatibility with realistic experimental setups. Under these constraints, the algorithm optimizes the population and phase distribution of a select number of low-lying rotational states in ultracold molecules to achieve maximum molecular orientation. The effectiveness of the proposed algorithm is demonstrated through numerical studies involving two- and three-state target subspaces, where the creation of a coherent superposition state with optimized population and phase distribution leads to the desired molecular orientation. Furthermore, its scalability is validated by application to a more complex 17-state subspace, where a maximum orientation value of 0.99055 is obtained, approaching the global optimal value of 1. Our findings demonstrate that by effectively managing these constraints, the influence of rotational states in the non-target state subspace can be substantially suppressed. A time-frequency analysis of the optimized pulses, coupled with the Fourier transform spectrum of the time-dependent degree of orientation, indicates that maximum molecular orientation is primarily attained through ladder-climbing excitation via multi-color pulse fields, with minimal contributions from highly excited states. This work serves as a valuable reference for designing experimentally feasible pulse fields using multi-constraint optimization algorithms, facilitating precise control over a limited number of rotational states to achieve maximum molecular orientation.
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Keywords:
- Quantum optimal control /
- Molecular orientation /
- Multiple constraints /
- Multiple objectives
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