Reduction-based strategy for optimal control of Bose-Einstein condensates

J. Adriazola, R. H. Goodman

Research output: Contribution to journalArticlepeer-review

Abstract

Applications of Bose-Einstein condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to the time-dependent Gross-Pitaevskii equation (GPE) model of BEC in multiple space dimensions, results in a large computational problem. We propose a control method based on first reducing the problem, using a Galerkin expansion, from a partial differential equation to a low-dimensional Hamiltonian ordinary differential equation system. We then apply a two-stage hybrid control strategy. At the first stage, we approximate the control using a second Galerkin-like method known as the chopped random basis to derive a finite-dimensional nonlinear programing problem, which we solve with a differential evolution algorithm. This search method then yields a candidate local minimum which we further refine using a variant of gradient descent. This hybrid strategy allows us to greatly reduce excitations both in the reduced model and the full GPE system.

Original languageEnglish (US)
Article number025311
JournalPhysical Review E
Volume105
Issue number2
DOIs
StatePublished - Feb 1 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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