Ground state energy of the $f=1$ spinor Bose-Einstein condensates

TL;DR

This paper calculates the ground state energy of spinor Bose-Einstein condensates with hyperfine spin f=1, including interactions, and resolves ultraviolet divergence issues using second-order perturbation methods.

Contribution

It provides a detailed calculation of the ground state energy for f=1 spinor BECs incorporating both repulsive and spin exchange interactions, and addresses divergence problems.

Findings

Ultraviolet divergence in energy corrections can be exactly eliminated.

Coupling constants are expressed in terms of s-wave scattering lengths.

The ground state energy is computed within the Bogoliubov approximation.

Abstract

We calculate, in the standard Bogoliubov approximation, the ground state energy of the spinor BEC with hyperfine spin $f=1$ where the two-body repulsive hard-core and spin exchange interactions are both included. The coupling constants characterized these two competing interactions are expressed in terms of the corresponding s-wave scattering lengths using second-order perturbation methods. We show that the ultraviolet divergence arising in the ground state energy corrections can be exactly eliminated.