Patterns and excitations in antiferromagnetic spinor condensates

We consider the phenomenon of spin-pattern formation reported in recent experiments in spin-2 rubidium condensate [J. Kronjager, C. Becker, P. Soltan-Panahi, K. Bongs, and K. Sengstock, Phys. Rev. Lett. 105, 090402 (2010)]. To understand the mechanism underlying the process and explain the parameters such as pattern period and growth rate, we employ the Bogoliubov-de Gennes equations and an alternative method based on energy conservation and the uncertainty principle. While the two methods agree in the spin-1 case, only the second method can provide analytical results in the spin-2 case. Using these results, we explain the occurrence of two regimes, the spin-dominated and the Zeeman-dominated, with the prevalence of spin-wave modes and quadrupole modes, respectively. We obtain very good agreement between theory and experiment for the pattern period and growth rate over several orders of magnitude of the magnetic field strength.