# Topologist Predicts New Form of Matter

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.

That’s puzzling. Surely the bonds that hold triplets together are the same as those that bind pairs. Actually, no! It turns out that there is a subtle but important difference that makes these bonds completely different.

Today, Nils Baas at the Norwegian University of Science and Technology makes another startling prediction. He says that the strange, unworldly bonds that allow cesium atoms to stick together in triplets should allow much more complex objects to form too. In fact, he says we’re on the verge of discovering a brand new form of matter governed by an entirely new branch of physics.

Behind this strange result is a branch of mathematics called topology, the study of shape. Topology is concerned in particular with the properties of shape that are preserved when an object is squeezed, stretched and pummelled, but not torn.

A useful example to consider is the famous Borromean ring shown above left. It consists of three circles intertwined in such a way that cutting one releases the other two.

A key point here is that the circles in a flat 2 dimensional plane cannot form a Borromean ring. But introduce a third dimension and all of a sudden the circles can be linked in this way. Of course, any flatlander living in this 2D plane would be utterly bamboozled by this property.

It turns out that there is formal mathematical analogy between the Borromean ring and the strange triplets of cesium that Efimov predicted. The mathematics of quantum mechanics and of topology turn out to be the same.

But here’s the thing: the bonds that emerge from the topology of quantum mechanics are entirely unworldly. While ordinary matter, the stuff you rap your knuckles on, is clearly confined to three dimensions, the mathematics of quantum mechanics exists in entirely different set of dimensions. And it’s in this space that the Borromean rings form.

The result is a kind of parallel physics, in which the laws governing behaviour in this parallel universe exert an inescapable, ghostly grip on our own universe.

And it’s not just the bonds between atoms that are effected. Physicists are beginning to build conductors and insulators in which the movement of electrons is governed by the topology of quantum mechanics. So-called topological insulators are a big topic in solid state physics right now.

And topology is about to extend its influence, if Baas has his way. He points out that Borromean rings are just the simplest example of an entire periodic table of topological structures. And if it’s possible to make Efimov states that are equivalent to Borromean rings, then it ought to be possible to make the others too.

This family of stuff will be a new state of matter that is governed by news rules, a kind of “Efimov physics”.

How might this stuff behave? That isn’t yet clear but Baas raises an interesting possibility. The deep and unworldly link between particles in Efimov states is remarkably similar to quantum entanglement.

Nobody’s quite sure if they’re identical but if they are, then Efimov physics will provide a new way to think about entanglement and how to generate and exploit it. That will have important implications for cryptography, computing and information science in general.

The Nobel Prize-winning physicist Murray Gell-Mann once stated that: “Everything not forbidden is mandatory.” He was referring to the way particles interact in quantum mechanics. In other words, if there’s no reason why particles cannot interact in a certain way, then they must interact in that way.

It looks as if we’re about to see how profound and far-reaching this statement really was.

Ref: arxiv.org/abs/1012.2698: New States of Matter Suggested By New Topological Structures