AUTHOR=Dionis E. , Peaudecerf B. , Guérin S. , Guéry-Odelin D. , Sugny D. 

TITLE=Optimal control of a Bose-Einstein condensate in an opticallattice: the non-linear and two-dimensional cases

JOURNAL=Frontiers in Quantum Science and Technology

VOLUME=Volume 4 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/quantum-science-and-technology/articles/10.3389/frqst.2025.1540695

DOI=10.3389/frqst.2025.1540695

ISSN=2813-2181

ABSTRACT=We numerically study the optimal control of an atomic Bose-Einstein condensate in an optical lattice. We present two generalizations of the gradient-based algorithm, GRAPE, in the non-linear case and for a two-dimensional lattice. We show how to construct such algorithms from Pontryagin’s maximum principle. A wide variety of target states can be achieved with high precision by varying only the laser phases setting the lattice position. We discuss the physical relevance of the different results and the future directions of this work.