We formulate a robust optimal control algorithm to synthesize minimum-energy pulses that can transfer a cold atom system into various momentum states. The algorithm uses adaptive linearization of the evolution operator and sequential quadratic programming to iterate the control towards a minimum-energy pulse that achieves optimal target state fidelity. Robustness to parameter variation is achieved using Legendre polynomial approximation over the domain of variation. The method is applied to optimize the Bragg beam splitting operation in ultracold atom interferometry. Even in the presence of 10–40% variability in the initial momentum dispersion of the atomic cloud and the intensity of the optical pulse, the algorithm reliably converges to a control protocol that robustly achieves unprecedented momentum levels with high fidelity for a single-frequency multiphoton Bragg diffraction scheme (e.g., $|\pm 40\hslash k\rangle$). We show the advantages of our method by comparison to stochastic optimization using sampled parameter values, provide detailed sensitivity analyses, and verify performance of the designed pulses in laboratory experiments.

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• Atom interferometry