Investigation of ground states of spin 1 bose einstein condensate in a harmonic trap

Abstract

In this thesis, we develop general methods to analytically obtain the ground state profiles and associated ground state properties of a spin-1 Bose-Einstein condensate under harmonic confinement with contact interaction. Firstly, from the Gross-Pitaevskii equation, we obtain the number density and energy density profiles of all possible stationary states using the Thomas-Fermi approximation for generic confinement. These stationary states compete to become the ground state in different parameter regimes. We show that a general method exists that can capture a lot of domain structures in a unified way. We show that by comparing the Thomas-Fermi approximated energy densities of different stationary states of a trapped system, under an essential constraint of the same chemical potential of the neighboring domains, one can actually capture the full spectrum of possible domain structures. While it is generally accepted that the Thomas-Fermi approximation is accurate for large condensates where the density is high enough to neglect the kinetic energy contribution compared to the interaction energies, we encounter situations, where even for large condensates, the Thomas-Fermi approximated predictions become inconclusive. We show that in the absence of the magnetic field, the Thomas-Fermi approximation predicts a ground state with which the other competing stationary states have a small energy difference, and the difference is of the order of the error introduced by the Thomas-Fermi approximation itself. Also in the presence of the magnetic field, for multi-component stationary states, the Thomas-Fermi approximation indicates domain structures in the ground state. In contrast, numerical simulations do not predict the same. The single-mode approximation, on the other hand, is also inaccurate in producing the sub-component profiles of the multi-component ground states. In such situations, one needs a multi-modal method to explain the ground state profiles and related properties analytically. We introduce a multi-modal