Stepwise Bose-Einstein Condensation in a Spinor Gas.

We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components m_{F}=0,±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}=±1, a phenomenon that cannot occur for an ideal gas with q>0.

Spontaneous formation and relaxation of spin domains in antiferromagnetic spin-1 condensates.

Many-body systems at low temperatures generally organize themselves into ordered phases, whose nature and symmetries are captured by an order parameter. This order parameter is spatially uniform in the simplest cases, for example the macroscopic magnetization of a ferromagnetic material. Non-uniform situations also exist in nature, for instance in antiferromagnetic materials, where the magnetization alternates in space, or in the so-called stripe phases emerging for itinerant electrons in strongly correlated materials. Understanding such inhomogeneously ordered states is of central importance in many-body physics. Here we study experimentally the magnetic ordering of itinerant spin-1 bosons in inhomegeneous spin domains at nano-Kelvin temperatures. We demonstrate that spin domains form spontaneously, that is purely because of the antiferromagnetic interactions between the atoms and in the absence of external magnetic forces, after a phase separation transition. Furthermore, we explore how the equilibrium domain configuration emerges from an initial state prepared far from equilibrium.