Spin fragmentation of Bose-Einstein condensates with antiferromagnetic interactions

TL;DR

This paper investigates how quadratic Zeeman effects influence spin fragmentation in antiferromagnetic spin-1 Bose-Einstein condensates, revealing a crossover from fragmented to polar condensate states dependent on atom number and temperature.

Contribution

It provides a detailed analysis of the crossover mechanism induced by quadratic Zeeman effects, highlighting the mesoscopic nature of spin fluctuations in finite atom number condensates.

Findings

Spin fragmentation is suppressed by quadratic Zeeman effect.

The crossover width scales as q ~ k_B T/N.

Spin fluctuations are observable in small atom number condensates.

Abstract

We study spin fragmentation of an antiferromagnetic spin 1 condensate in the presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry. We describe how the QZ effect turns a fragmented spin state, with large fluctuations of the Zeemans populations, into a regular polar condensate, where atoms all condense in the $m=0$ state along the field direction. We calculate the average value and variance of the Zeeman state $m=0$ to illustrate clearly the crossover from a fragmented to an unfragmented state. The typical width of this crossover is $q \sim k_B T/N$, where $q$ is the QZ energy, $T$ the spin temperature and $N$ the atom number. This shows that spin fluctuations are a mesoscopic effect that will not survive in the thermodynamic limit $N\rightarrow \infty$, but are observable for sufficiently small atom number.