Interfaces in spinor Bose-Einstein condensates
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Bose-Einstein condensates - a state of matter at low temperature in which a macroscopic amount of bosons occupy the quantum-mechanical ground state- were originally trapped magnetically. The drawback of this trapping method is that only the weak-ﬁeld seeking spin state is trapped and we therefore only have a one component i.e. scalar condensate. In contrast, optical trapping conﬁnes atoms of all spin state and therefore allows for spin degrees of freedom, resulting in spinor Bose Einstein condensates. In this thesis, density proﬁles of these spinor condensates have been calculated in Thomas-Fermi approximation. The proﬁles show areas with strict phase separation, but also areas with spin mixtures. For sodium atoms we get a strict separation between the mF = ±1 and the mF = 0 spin state in Thomas-Fermi approximation. This however causes discontinuities in the transition between spin domains and thus these interfaces were studied further. We found that the density proﬁle of a spin state behaves roughly like a hyperbolic tangent at such an interface. Finally, a diﬀerential equation is proposed that could be solved as a starting point of follow-up research.