Exploring Spinor Bose-Einstein Condensates in and beyond the Single Mode Approximation

Spinor gases are a promising system of exploring quantum entanglement, a phenomena significant in the fields of quantum sensing and computation. The large difference in energy scales in scattering between internal states and kinetic dynamics allows one to neglect fluctuations in the density profiles of spinor gases over timescales relevant for spin dynamics. This is known as the single-mode approximation, which has proven fruitful in theoretical analysis and is a starting point for many works. Here we explore effects not described by the single-mode approximation, both in the mean-field via simulation of the Gross-Pitaevskii equation and in beyond mean-field theory computation.