Spin dynamics beyond the single mode approximation in a sodium spinor BEC*

We use a sodium spin-1 Bose-Einstein condensate to experimentally demonstrate that physics beyond the single-mode approximation can be relevant during the short-time non-equilibrium dynamics. Our experiments rely on microwave dressing of the F=1 hyperfine states, where F denotes the total angular momentum of the Na atoms. The observed spin population dynamics are compared to theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations. The fact that beyond single-mode approximation physics can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as non-linear SU(1,1) interferometers. Our work opens the door for devising time-dependent coupling schemes between spin and spatial degrees of freedom.