Quantum Mechanics returns to Ancient Greece

For a hundred years now, we have known that some compounds lose their electrical resistance at low temperatures, a phenomenon known as superconductivity. Electrical current flows without resistance in these materials, offering unique possibilities such as carrying electrical current without loss or storing electrical energy for a nearly infinite time. However, even for the ¡°hottest¡± compounds (known as high critical temperature superconductors), superconductivity only appears below ?150 degrees Celsius, a temperature way too low for large-scale practical applications.

The major obstacle to the synthesis of superconducting materials at room temperature is the absence of a reliable theoretical description of the microscopic behaviour of electrons in high critical temperature compounds, without which physicists are reduced to groping for new chemical compounds working at higher temperatures. Although J. Bardeen, L. Cooper and J. Schrieffer proposed the BCS model, which describes superconductivity in metals at low temperatures fifty years ago, their theory does not apply to recent high critical temperature materials. In the BCS theory, electrons are supposed to be weakly interacting, while they interact strongly in these new superconductors. The understanding of high critical temperature superconductivity is therefore highly challenging, since it must describe the dynamics of a huge number (about 10²³ electrons per cubic centimetre), interacting strongly, while taking into account quantum mechanics, which confers both particle and wave properties to electrons and is necessary for the emergence of superconductivity. This problem is so demanding that, even today, after months of computation, the most powerful computers can only describe the dynamics of a hundred electrons.

Faced with this challenge, Nobel Prize winner R.P. Feynman suggested in the early 80s that it would be possible to overcome the computation time problem by simply abandoning conventional digital computers and using analogue computers. As their name suggests, analogue computers are based on analogies. To solve a given mathematical problem, one tries to find a physical system whose behaviour matches the equations of the problem as closely as possible, and obtains a solution by making measurement on the system. This method of computing is actually ancient, and can be traced back to Greek antiquity. For example, the Antikythera mechanism, from 150 BC, is a cogwheel assembly that was used to predict the position of stars and planets. It constitutes the ancestor of Middle Age astronomical clocks, and more refined variations of this scheme were used until the 1950s for ballistic computations or calculation of tidal amplitudes.

The past few years have demonstrated that laser cooled atoms can be used as accurate simulators of solid state physics. Indeed, progress in laser cooling and trapping of atoms with light have allowed us to reach temperatures low enough to observe phenomena analogous to superconductivity. In 2004, our group in Paris, as well as groups in Boulder, Innsbruck and MIT have reproduced the physical conditions of weakly interacting superconductors described by BCS theory, not with electrons but with atomic vapour. These experiments confirmed and extended the BCS model, since interatomic interactions can be tuned to the strongly interacting regime, by contrast with electrons whose electric charge is fixed.

To fully reproduce high critical temperature superconductors, their atomic counterpart needs an additional ingredient. Experiments on electrons have shown that the crystal lattice orients the motion of the electrons, and plays a central role in this type of superconductor. To reproduce these experimental conditions, we can trap atoms in an ¡°optical lattice¡±¡ªa tridimensional lattice of tiny atom traps created by the interference^[1] of several laser beams. Although this new generation of experiments has not yet achieved temperatures low enough to obtain high critical temperature superconductivity, physicists in Mainz and Zurich have observed one of the salient features of these compounds. We know that superconductivity, surprisingly, vanishes in these compounds when the electron density is too large. The atoms block each other¡¯s paths, and prevent transport of electrical current. This phase is called a Mott insulator and was observed in ultra-cold gases, thus confirming the ability of these systems to simulate solid state physics.

After these initial breakthroughs, many original schemes were proposed to further cool ultra-cold gases trapped in optical lattices, to finally reach the high critical temperature regime. If these new experiments succeed, they will offer new insights into the properties of high critical temperature materials and may even show us the way to new compounds carrying electrical current without loss at room temperature.

[1] Interference between multiple light rays produces a periodic modulation of light intensity, and are, for example, responsible for the irisations seen at the surface of soap bubbles.