Multicomponent states for trapped spin-1 Bose-Einstein condensates in the presence of a magnetic field

In the presence of a magnetic field, multicomponent ground states appear in trapped spin-1 Bose-Einstein condensates for both ferromagnetic and antiferromagnetic types of spin-spin interaction. We aim to produce an accurate analytical description of the multicomponent states which is of fundamental importance. Despite being in the so-called regime of the Thomas-Fermi approximation (condensates with large particle number), the scenario of multicomponent states is problematic under this approximation due to the large variation in densities of the subcomponents. We generalize the variational method that we have introduced [P. K. Kanjilal and A. Bhattacharyay, Eur. Phys. J. Plus 137, 547 (2022)] to overcome the limitations of the Thomas-Fermi approximation. We demonstrate that the variational method is crucial in identifying multicomponent ground states. A comparison of the results of the variational method, which is multimodal by construction, with that of the single-mode approximation is also presented in this paper to demonstrate a marked improvement in accuracy over the single-mode approximation. We have also looked into the phase transition between phase-matched and polar states in a trapped condensate using the variational method and have identified substantial change in the phase boundary. The correspondence of the phase diagram of the trapped case with the homogeneous one identifies other limitations of the Thomas-Fermi approximation as opposed to the more accurate variational method.