Analytic models for density of a ground-state spinor condensate

TL;DR

This paper develops analytic models for the ground-state densities of various spinor Bose-Einstein condensates using the Thomas-Fermi approximation, simplifying the coupled equations to decoupled forms and validating with numerical solutions.

Contribution

It introduces simplified analytic models for ground-state densities of spinor BECs by decoupling the GP equations and applying the Thomas-Fermi approximation, applicable to ferromagnetic, anti-ferromagnetic, and cyclic states.

Findings

Analytic models closely match numerical solutions.

Decoupled GP equations effectively approximate ground states.

Models applicable to realistic experimental parameters.

Abstract

We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi approximation (TFA) to this decoupled equation. Similarly, for the ground states of spin-1 anti-ferromagnetic and spin-2 anti-ferromagnetic and cyclic BECs, some of the spin component densities are zero which reduces the coupled GP equation to a simple reduced form. Analytic models for ground state densities are also obtained for anti-ferromagnetic and cyclic BECs from the TFA to the respective reduced GP equations. The analytic densities are illustrated and compared with the full numerical solution of the GP equation with realistic experimental parameters.