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Quantum systems of many interacting particles at low temperatures generally organize themselves into ordered phases of matter, whose nature and symmetries are captured by an order parameter. In the simplest cases, this order parameter is spatially uniform. For example, a system of localized spins with ferromagnetic interactions align themselves to a common direction and build up a macroscopic magnetization on large distances. However, non-uniform situations also exist in nature, for instance in antiferromagnetism where the magnetization alternates in space. The situation becomes even richer when the spin-carrying particles are mobile, for instance 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. In this work, 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 after a phase separation transition, textit{i.e.} in the absence of external magnetic force, purely because of the antiferromagnetic interactions between the atoms. Furthermore, we explore how the equilibrium domain configuration emerges from an initial state prepared far-from-equilibrium.
Large spin systems can exhibit unconventional types of magnetic ordering different from the ferromagnetic or Neel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invarianc
We numerically simulate the creation process of two-dimensional skyrmionic excitations in antiferromagnetic spin-1 Bose--Einstein condensates by solving the full three-dimensional dynamics of the system from the Gross--Pitaevskii equation. Our simula
Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obtained for integrable models. In this paper, we present four families o
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 Zee
We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on the spin-1 Bose-Einstein condensates. By solving the stochastic projected Gross-Pitaevskii equation,