Solitons on the surface of a sphere

Kurzfassung

The recent realization of ultracold quantum gases in a shell geometry [1] paves the way towards a Bose-Einstein condensate (BEC) that is trapped tightly onto the surface of a sphere. We investigate the existence and stability of solitons that appear in this system using the two-dimensional (2D) Gross-Pitaevskii equations (GPE). Comparing our results to the 2D plane, we find that the scale invariance of the GPE is broken due to the curvature and compactness of the shell geometry. Consequently, the familiar Townes solitons [2] appear only when the BEC is strongly localized in a small region of the sphere surface. [1] R. A. Carollo et al., Nature (London) 606, 281 (2022). [2] B. Bakkali-Hassani et al., Phys. Rev. Lett. 127, 023603 (2021).