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ORIGINAL RESEARCH article

Front. Quantum Sci. Technol.
Sec. Quantum Engineering
Volume 4 - 2025 | doi: 10.3389/frqst.2025.1540695
This article is part of the Research Topic Recent Advances in Quantum State Engineering using Atoms and Photons View all articles

Optimal control of a Bose-Einstein Condensate in an optical lattice: The non-linear and the two-dimensional cases

Provisionally accepted
Etienne Dionis Etienne Dionis 1Bruno Peaudecerf Bruno Peaudecerf 2Stéphane Guérin Stéphane Guérin 1David Guéry-Odelin David Guéry-Odelin 2Dominique Sugny Dominique Sugny 1*
  • 1 Université de Bourgogne, Dijon, France
  • 2 Université de Toulouse, Toulouse, Midi-Pyrénées, France

The final, formatted version of the article will be published soon.

    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 nonlinear 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.

    Keywords: optimal control theory, Bose-Einstein Condensates, Gross-Pitaevskii Equation, Grape, FBD-DVR

    Received: 06 Dec 2024; Accepted: 03 Jan 2025.

    Copyright: © 2025 Dionis, Peaudecerf, Guérin, Guéry-Odelin and Sugny. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Dominique Sugny, Université de Bourgogne, Dijon, France

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