Is it something unexpected?Why universality in cold atomic gases is important?What researches are looking for?Can this be useful for topological quantum computers?
Can we expect a whole myriad of these states?
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Efimov physics is interesting because it's a neat bit of fundamental physics describing something we have a tendency to neglect: 3-body quantum scattering problems. As for being unexpected -- I'm not sure what you want; if Efimov states were expected then V.N. Efimov wouldn't have had to discover them (already more than 40 years ago!). The experimental verification was not unexpected, but did have to wait for the right tools to emerge.
Which brings me to my next point -- I've seen the paper that you linked to; I don't have the ability to judge its merits as a topology paper, but it is not a physics paper. If you are interested in learning about Efimov physics, then this paper is a gentle introduction with solid references if you are serious.
While Efimov states share an interesting "feature" of three-body bound states even when no two of the bosons would be bound (analogous to the Borromean rings) this has nothing to do with nontrivial topological properties that would be used for quantum computation.
Edit: It's also worth noting, in retrospect, that there exists an analogous phenomenon in 4-body physics: recently it was noticed that for every Efimov trimer, there are two corresponding tetramers. I think some people conjecture that there are similar any $N>2$-body Efimov states, which seems to me still rather different from the logic of the paper in the original question.