Nematic ordering dynamics of an anti-ferromagnetic spin-1 condensate

We consider the formation of order in a quasi-two-dimensional (quasi-2D) anti-ferromagnetic spin-1 condensate quenched from an easy-axis (EA) to an easy-plane (EP) nematic phase. We define the relevant order parameter to quantify the spin-nematic degrees of freedom and study the evolution of the spin-nematic and superfluid order during the coarsening dynamics using numerical simulations. We observe dynamical scaling in the late time dynamics with both types of order extending across the system with a diffusive growth law. We identify half-quantum vortices (HQVs) as the relevant topological defects of the ordering dynamics, and demonstrate that the growth of both types of order is determined by the mutual annihilation of these vortices.