Mapping a Spin Dynamics Resonance Beyond the Single-mode Approximation in a Sodium Spinor Bose-Einstein*

We present experiments on a resonant coupling between spin and spatial degrees of freedom beyond the single-mode approximation (SMA) during short time non-equilibrium dynamics in a sodium spin-1 Bose-Einstein Condensate. Our quench-induced spin oscillation experiments rely on microwave dressing of the F = 1 hyperfine states where F denotes the total angular momentum of the Na atoms. Our data shows a slow baseline drift of the spin oscillation when the effective quadratic Zeeman shift q is tuned via microwave dressing to certain values. The baseline drift occurring at certain values of q indicates spin dynamics beyond the SMA. Our data agrees well with recent theory, based on a q-dependent, resonant coupling between spin and spatial degrees of freedom. We further explore these effects by scanning q around the point of maximum baseline drift to map out the the width of the complete resonance phenomenon as a function of q. This research has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for non-linear SU(1,1) interferometers.