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How can a single-mode approximation be justified in spinor F=1 BEC with dipole-dipole interactions? Or maybe this kind of approximation will never take place and condensate components are always separated. What do You think?

Good literature on the topic is welcome.

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In the field of multi-component condensates, the single mode approximation (SMA) means that different dipole states are assumed to share the same spatial wave function. Thus, there are no dipolar textures.

SMA is well justified when the inter-component (e.g., spin-dependent or dipole) interactions are much weaker than the interactions independent of the components.

My guess is that the OP is concerned about the applicability of the SMA for ultracold atoms due to their experience with solid-state physics, where even a weak dipolar interaction spontaneously induces spatially varying dipole moments.

Indeed, the SMA is not always applicable for BECs. My favorite reference on the topic is cond-mat/0606099 , they give phase diagrams, explicitly showing where the SMA is applicable, and when it breaks down. More references can be found in a recent paper arXiv:1306.0398 , and also in papers citing the first paper.

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