Winding real and order-parameter spaces via lump solitons of spinor BEC on sphere

TL;DR

This paper explores topological lump solitons in spinor Bose-Einstein condensates on spherical shells, revealing their quantized winding numbers and energy properties, with implications for cold-atom experiments.

Contribution

It provides explicit lump-soliton solutions and analyzes their energy and topological properties, advancing understanding of topological excitations in spinor BECs on spherical geometries.

Findings

Lump solitons have quantized winding numbers.

Higher-winding lumps are energetically competitive with multiple lower-winding lumps.

Predictions are testable in cold-atom experimental setups.

Abstract

The three condensate wavefunctions of a spinor BEC on a spherical shell can map the real space to the order-parameter space that also has a spherical geometry, giving rise to topological excitations called lump solitons. The homotopy of the mapping endows the lump solitons with quantized winding numbers counting the wrapping between the two spaces. We present several lump-soliton solutions to the nonlinear coupled equations minimizing the energy functional. The energies of the lump solitons with different winding numbers indicate coexistence of lumps with different winding numbers and a lack of advantage to break a higher-winding lump soliton into multiple lower-winding ones. Possible implications are discussed since the predictions are testable in cold-atom experiments.