Resonances between spin dynamics and spatial excitations in non-equilibrium spinor Bose-Einstein condensates

Spinor Bose-Einstein condensates possess a rich phase diagram that provides a versatile platform for a tunable implementation of a quantum simulator. Spin changing collisions between spin states within spinor condensates provide a simple way to produce entanglements, finding broad applications in quantum technologies. The energy scale separation between spatial and spin degrees of freedom allows one to engineer the spin dynamics by avoiding spatial excitations. The assumption of a single-spatial model is broken for specific values of external parameters for which the spin dynamics is involved with the occurance of complicated spatial structures. Therefore, it is vital to understand the resonance between the spatial excitations and spin degrees of freedom of the system. This work introduces a few-spatial-mode framework to model the spin dynamics of spinor Bose-Einstein condensates, aiming in particular to capture the resonances with different types of spatial excitations, including those with a single-particle nature and those with particle-hole correlations.