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Cold fermions could simulate superconductors

11 Sep 2008 Margaret Harris
Metallic and Mott insulating states

Physicists in Switzerland and France have produced a gas of cold, trapped atoms which mimics features of solid-state superconductors. By confining potassium atoms at temperatures a fraction of a degree above absolute zero in a pattern of deep potential wells – similar to eggs in an egg carton — researchers led by Tilman Esslinger at ETH Zurich have created the first example of fermionic atoms behaving like a Mott insulator.

A Mott insulator forms when interactions between electrons in a crystalline solid prevent the conduction electrons from moving freely between atoms. Many important phenomena in condensed matter physics, including high-temperature superconductivity, occur when the material is nearly in a Mott insulating phase. The reasons for the transition to high-temperature superconductivity are not fully understood, however, and applying the reigning theoretical model (known as the Hubbard model) to complex solids at relatively high temperatures creates computational headaches.

‘Quantum simulators’

Atomic systems like the potassium lattice in Zurich are far simpler and easier to manipulate, and can be used as “quantum simulators” in which one quantum system imitates the behaviour of a more complex one. In the atomic analogue to a Mott insulator, intersecting laser beams form a crystal-like “optical lattice” of potential wells, with one atom in each well. If the wells are deep enough, atoms can no longer hop or tunnel between lattice sites and an “insulator” is formed.

What we do is to simulate this very interesting quantum system in a more controlled fashion Henning Moritz, ETH Zurich

The first atomic Mott insulator was created in 2002 by researchers at Munich using ultracold bosonic rubidium atoms. But electrons are fermions, so the Zurich experiment is one step closer to a quantum simulator for solid-state systems, says Henning Moritz, an author of the Zurich group’s paper, which appeared in Nature on 11 September.

Difficult to observe

Bosons undergo an abrupt and relatively easy-to-detect phase transition from a Bose-Einstein condensate to a Mott insulator. Such a transition does not occur in fermions due to differences in their quantum properties, so the onset of the Mott insulator is harder to observe directly.

Instead, the Zurich team demonstrated that almost none of the lattice sites in their experiment were occupied by more than one atom — a key requirement for a Mott insulator to exist (Nature 455 204 ).

To do this, they first exploit a phenomenon known as a Feshbach resonance to make pairs of atoms repel each other, so that even fermions in different spin states (which can have the same energy under the Pauli exclusion principle) are no longer as “happy” to share the same lattice site. The trapped atoms are then subjected to a pulse of radio frequency light, which flips the spins of one atom in every pair, but leaves lone atoms untouched. By recording “shadow” images of atoms in different spin states, the team was able to show that only 1% of lattice sites contained more than one atom.

They definitely see very nice evidence of strong interactions between the particles suppressing double occupation, but in my view this is not sufficient for proving a Mott insulating state Immanuel Bloch, University of Mainz

More to be done

Some scientists sounded a note of caution about the result. “They definitely see very nice evidence of strong interactions between the particles suppressing double occupation, but in my view this is not sufficient for proving a Mott insulating state,” says Immanuel Bloch of the University of Mainz, who led the team which demonstrated the first atomic Mott insulator. Another key requirement, he says, is to show that the system cannot be compressed – besides having no doubly-occupied sites, the lattice also must not have “holes”. A related paper by Bloch and colleagues at Mainz and Cologne, in which they describe a competing method for creating and detecting a Mott insulator in atomic fermions, appeared yesterday as a preprint on the arXiv preprint server (arXiv:0809.1464).

Moritz accepts that the Zurich experimenters have no direct evidence of an incompressible or “hole-free” lattice, but says that their system is cold enough that few holes can exist. “A direct measurement of compressibility would be a beautiful thing, but even without that we are very clear that what we have seen is only consistent with a Mott insulator,” he says.

Both Moritz and Bloch agree that a Mott insulator is only the first step towards using cold atoms to test our understanding of high-temperature superconductivity. The next landmark, Moritz says, would be to demonstrate an antiferromagnetic Mott insulator, in which fermionic atoms in neighbouring lattice sites have opposite spins, and can therefore hop between lattice sites for brief periods.

Turn down the heat

To achieve this, experimentalists need to produce temperatures two or three times colder than have so far been reached for fermions, Bloch said, while imitating high-temperature superconductivity would probably require a further factor of 100.

Still, the current result is important, Moritz said, because it represents a new way of studying solid-state systems. “What we do is to simulate this very interesting quantum system in a more controlled fashion,” he said.

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