We propose a methodology to design optimal pulses for achieving quantum optimal control on molecular systems. Our approach constrains pulse shapes to linear combinations of a fixed number of experimentally relevant pulse functions. Quantum optimal control is obtained by maximizing a multi-target fitness function using genetic algorithms. As a first application of the methodology, we generated an optimal pulse that successfully maximized the yield on a selected dissociation channel of a diatomic molecule. Our pulse is obtained as a linear combination of linearly chirped pulse functions. Data recorded along the evolution of the genetic algorithm contained important information regarding the interplay between radiative and diabatic processes. We performed a principal component analysis on these data to retrieve the most relevant processes along the optimal path. Our proposed methodology could be useful for performing quantum optimal control on more complex systems by employing a wider variety of pulse shape functions.
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We used δt = 1.875 × 10−1 and ω ≈ 9 × 10−3 in our numerical simulation in Section III.
The probability of occurrence of a genetic operation, πM(πX), is defined as follows: first, generate a random number from the uniform distribution between zero and one; second, if this number is lower than πM(πX), the operation is performed. The probabilities πM = 0.15 and πX = 0.8 were used in this work.
It is crucial to limit the generation of the initial list of individuals to the region of the parameters space with experimental relevance.
A diabatic representation of the dynamics was used through the paper.
