Quantum elliptic vortex in the polar phase of a spin-1 Bose-Einstein condensate

A novel topological defect in a spin-nematic superfluid is found theoretically. A quantized vortex spontaneously breaks its axisymmetry, leading to an elliptic vortex in the polar phase of spin-1 Bose-Einstein condensates of ²³Na gasses with small quadrative Zeeman shift. The new vortex is considered the Joukowski transform of a conventional vortex. Its oblateness grows when the Zeeman length exceeds the spin healing length. This structure is sustained by balancing the hydrodynamic potential and the elasticity of a soliton connecting two spin spots, which are observable by in situ magnetization imaging. The theoretical analysis clearly defines the difference between half quantum vortices of the polar and anti-ferromagnetic phases in spin-1 condensates. This work is motivated by and related to the recent experiments on wall-vortex composite defects by Shin's group in Seoul National University [Phys. Rev. Lett. 122, 095301 (2019) and Phys. Rev. A, 101, 023613 (2020)].