The dynamics of quantum phases in a spinor condensate

TL;DR

This paper analyzes the quantum phases and their diffusion dynamics in a spinor-1 Bose-Einstein condensate, revealing how phase fluctuations and symmetries evolve under ferromagnetic interactions and external magnetic fields.

Contribution

It provides an exact ground state distribution of phases and discusses the dynamic recovery of broken symmetries in a spinor-1 condensate with ferromagnetic interactions.

Findings

Mean field ground state is stable against atom number fluctuations.

Phases diffuse but recover symmetries when N and M are conserved.

External magnetic fields influence quantum dynamics.

Abstract

We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground state distribution of the phases associated with the total atom number ($N$), the total magnetization (${\cal M}$), and the alignment (or hypercharge) ($Y$) of the system. The mean field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recover the two broken continuous symmetries [U(1) and SO(2)] when $N$ and ${\cal M}$ are conserved as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with anti-ferromagnetic interactions.