We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between Efimov states in cold gases and Borromean and Brunnian rings to these new higher order links. This gives rise to a hole new hierarchy of possible states with Efimov states at the bottom.
MIT Technology Review - A link between quantum mechanics and topology implies the existence of an entirely new state of matter. And physicists have already found the first example.
Back in 1970, a young physicist working in the Soviet Union made a counterintutive prediction. Vitaly Efimov, now at the University of Washington in the US, showed that quantum objects that cannot form into pairs could nevertheless form into triplets.
In 2006, a group in Austria found the first example of such a so-called Efimov state in a cold gas of cesium atoms.
It would be very interesting if one could nd a connection between the topology of
these higher order links and the quantum entanglement. For a discussion of
more general manybody system interactions.
Let us conclude by mentioning that it is a natural and interesting question whether
the higher order links we have introduced may be synthesized as molecules. Trefoil
knots and Borromean rings have been synthesized by very sophisticated
techniques. To synthesize higher order links is a daunting task, but for example Borromean rings of Borromean rings and other members of the families we have defi ned like kB(n1; : : : ; nk) and kH (n1; : : : ; nk) in Section 6 may be possible to synthesize by using DNA molecules and the techniques developed by Ned Seeman.
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