Manifestation of a gap due to the exchange energy in a spinor condensate

We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between the results obtained in the Bogoliubov–Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We verify that, contrary to the BPA, the GRPA preserves the SU(2)SU(2) symmetry and the ff-sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap.