Mean field ground state of a spin-1 condensate in a magnetic field

TL;DR

This paper analyzes the mean field ground state of a spin-1 atomic condensate in a magnetic field, emphasizing the quadratic Zeeman effect's role in energy balance under conserved atom number and magnetization.

Contribution

It revisits the mean field ground state considering magnetic field effects and examines the validity of the single spatial mode approximation in this context.

Findings

Quadratic Zeeman effect significantly influences the energy balance.

The SMA's dependence on magnetic field and magnetization is characterized.

Conservation of N and M constrains the ground state configurations.

Abstract

We revisit the topic of the mean field ground state of a spin-1 atomic condensate inside a uniform magnetic field ($B$) under the constraints that both the total number of atoms ($N$) and the magnetization ($\cal M$) are conserved. In the presence of an internal state (spin component) independent trap, we also investigate the dependence of the so-called single spatial mode approximation (SMA) on the magnitude of the magnetic field and ${\cal M}$. Our result indicate that the quadratic Zeeman effect is an important factor in balancing the mean field energy from elastic atom-atom collisions that are known to conserve both $N$ and $\cal M$.