New insights into a popular and potentially useful model of how electrons behave in solids have been provided by an experiment involving ultracold atoms. Markus Greiner and colleagues at Harvard University in the US studied the behaviour of lithium-6 atoms that are held in an optical lattice and interact according to rules set out by the Fermi-Hubbard model.

They found that the system becomes magnetic at low temperatures – and that the magnetism disappears when the density of atoms is reduced. The team can now use its atomic simulator to explore regimes of the Fermi-Hubbard model that could harbour very interesting physics including high-temperature superconductivity.

The electronic properties of solid materials arise from quantum-mechanical interactions between large numbers of electrons. It is notoriously difficult to calculate these properties, so physicists rely on simple models to simplify the mathematics – but even models have significant computational challenges. One such scheme is the Fermi-Hubbard model, which represents electrons as Fermi–Dirac particles (fermions) that hop between fixed sites on a lattice and only interact with each other when they occupy the same lattice site.

Dimensional difficulties

Despite its simplicity, the quantum nature of fermions means that meaningful calculations are only possible for 1D chains of lattice sites. Even calculations on 2D lattices – which could by very useful for understanding high-temperature superconductors – have proven extraordinarily difficult to achieve.

One possible way around this problem is to use a physical system of real particles to simulate the Fermi-Hubbard model – effectively doing an experiment to mimic a model that describes another physical system. Greiner and colleagues have used an ensemble of lithium-6 atoms, which are fermions and therefore obey the same quantum-mechanical rules as electrons. The team created their simulation by criss-crossing laser beams to make a square lattice of potential wells, each of which can hold an atom.

While this approach is not new, it had previously been very difficult to reduce the temperature of the atoms such that they behaved like electrons in a solid. Although previous attempts had chilled the atoms to just a tiny fraction of a kelvin, their thermal motions were on par with electrons in a solid heated about 1000 K. This is much hotter than the 100–200 K below which high-temperature superconductivity occurs, and is also too hot for the emergence of magnetism.

Under the microscope

Greiner and colleagues overcame the temperature problem by surrounding the optical lattice with a sea of atoms that act as a coolant. They also used an optical system dubbed a "fermionic microscope" to monitor individual lattice sites.

The team found that when the lattice was full – or nearly full – of atoms, the system behaved as an antiferromagnetic insulator. According to Thierry Giamarchi of the University of Geneva in Switzerland, who was not involved in the experiment, it is the first time that a system has been cooled sufficiently to create a magnetic state with long-range order. As the number of atoms is decreased, the magnetic state is seen to disappear.

It is in this low-density regime that a state resembling a high-temperature d-wave superconductor is expected to exist – albeit at a lower temperature than is currently accessible to Greiner's team. Writing in Nature, the team points out that it should be possible to further cool the atoms to reach the superconducting state.