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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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