Rotation of a Bose-Einstein Condensate held under a toroidal trap

The aim of this paper is to perform a numerical and analytical study of a rotating Bose Einstein condensate placed in a harmonic plus Gaussian trap, following the experiments of \cite{bssd}. The rotational frequency $\Omega$ has to stay below the trapping frequency of the harmonic potential and we find that the condensate has an annular shape containing a triangular vortex lattice. As $\Omega$ approaches $\omega$, the width of the condensate and the circulation inside the central hole get large. We are able to provide analytical estimates of the size of the condensate and the circulation both in the lowest Landau level limit and the Thomas-Fermi limit, providing an analysis that is consistent with experiment.

💡 Research Summary

The paper presents a combined numerical and analytical investigation of a Bose‑Einstein condensate (BEC) rotating in a two‑dimensional trap that consists of a harmonic confinement superimposed with a central Gaussian barrier, thereby creating a toroidal geometry. The study is motivated by recent experiments (referenced as bssd) that observed annular condensates with triangular vortex lattices when the rotation frequency Ω is kept below the harmonic trap frequency ω. As Ω approaches ω, the condensate expands radially, the central hole widens dramatically, and the circulation around the hole increases.

The authors start from the Gross‑Pitaevskii equation (GPE) in the rotating frame:

iℏ∂ψ/∂t =