Stepwise Bose-Einstein condensation in a spinor gas

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 $q>0$.