Surrogate-assisted three-dimensional Gross-Pitaevskii characterization of Bose-Einstein condensate transport on an atom chip

Abstract

We develop a surrogate-assisted workflow for millimeter-scale transport of a $^{87}$Rb Bose--Einstein condensate (BEC) on a multi-wire atom chip. Gradient-based inverse optimization generates 42 current schedules spanning seven regularization strengths and six transport durations. A low-cost Gaussian phase-space model ranks these schedules by endpoint overlap at three atom numbers. A Thomas--Fermi scaling (Ermakov) model estimates cloud dimensions for case-specific moving-grid construction. We then evaluate selected schedules in detail with the three-dimensional Gross--Pitaevskii equation (GPE). At $N=10^3$ and $T=0.5$ s, the surrogate predicts a larger axial center-of-mass (COM) excursion than at longer durations. The GPE confirms this prediction and reveals sloshing that persists through delivery, with an endpoint fidelity $F_{3D}=0.9244$. For all five longer transports, the surrogate predicts near-unit endpoint overlap for the top-ranked schedules, and GPE propagation using these schedules gives $F_{3D}>0.9997$. At $N=10^4$ and $T=2.0$ s, the surrogate-selected schedule similarly gives $F_{3D}=0.999932$. These results demonstrate that the surrogate estimates provide a useful low-cost basis for candidate screening, while GPE propagation resolves the transport dynamics and the delivered condensate state.