Spin domains in ground state of a trapped spin-1 condensate: A general study under Thomas-Fermi approximation

Investigation of ground state structures and phase separation under confinement is of great interest in spinor Bose Einstein Condensates (BEC). In this paper we show that, in general, within the Thomas-Fermi (T-F) approximation, the phase separation scenario of stationary states can be obtained including all the mixed states on an equal footing for a spin-1 condensate for any confinement. Exact analytical expressions of energy density, being independent of local mass density for all allowed states enables this general analysis under T-F approximation. We study here in details a particular case of spherically symmetric harmonic confinement as an example and show a wide range of potential phase separation scenario for anti-ferromagnetic and ferromagnetic interactions.