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Inhomogeneous spin domain induced by the quadratic Zeeman effect in spin-1 Bose-Einstein condensate

We show two kinds of inhomogeneous spin domain possessing Néel-like domain walls in spin-1 Bose-Einstein condensate, which are induced by the positive and negative quadratic Zeeman effect (QZE) respectively. In both cases, the spin density distribution is inhomogeneous and has zeros where the magnetization vanishes. For positive and negative QZE, the spin patterns and topological structures are remarkably different. Such phenomena are due to the pointwise different axisymmetry-breaking caused by the pointwise different population exchange between the sublevels, arising uniquely from the QZE. We analyze in detail the inhomogeneous domain formation and related experimental observations for the spin-1 $^{87}$Rb and $^{23}$Na condensate.