# Stepwise Bose-Einstein condensation in a spinor gas

## TL;DR

This paper reports the observation of multi-step Bose-Einstein condensation in a spinor gas of sodium atoms, revealing how the sequence and nature of condensation depend on magnetization and quadratic Zeeman energy, with interactions significantly affecting the phase diagram.

## Contribution

It provides the first detailed experimental study of stepwise BEC in a spinor gas, highlighting the effects of interactions and magnetic field parameters on the condensation sequence.

## Key findings

- Multi-step condensation observed in sodium spinor gas.
- Sequence depends on magnetization and quadratic Zeeman energy.
- Interactions significantly alter phase diagram compared to ideal gas.

## Abstract

We observe multi-step condensation of sodium atoms with spin $F=1$, where the different Zeeman components $m_F=0,\pm 1$ condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization $m_z$ and on the quadratic Zeeman energy $q$ (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin 1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading for instance to condensation in $m_F=\pm 1$, a phenomenon that cannot occur for an ideal gas with $q>0$.