From sandpiles to neutron stars, the understanding of the behaviour of many body systems is one of the major challenges of modern physics. When the actors follow the rules of the quantum world, such as electrons in solids, the problem becomes so involved than even the most powerful computers available in a foreseeable future are helpless. Faced with this deadlock, Nobel prize winner R.P. Feynman suggested in the early 80’s that for such complicated problems, conventional digital computers could be replaced by analog simulators : to solve complex mathematical equations, one should design a physical system obeying precisely to the equations under study and obtain their solutions by making appropriate experimental measurements.
This scheme was recently implemented in Laboratoire Kastler Brossel at Ecole normale supérieure (ENS) in Paris in the case of a cloud of strongly interacting fermions  : Using laser manipulation techniques, C. Salomon’s team at ENS has determined the thermodynamic equation of state of a gas of particles with short range interactions. This equation is universal and applies to ultra-cold atomic gases, as well as the upper crust of neutron stars.
The study realized at ENS can be extended to a wealth of systems relevant to quantum gas experiments and demonstrates the depth of Feynman’s program. In the long term, one of the challenges of the field would be to use the techniques developped at ENS as well as in other international groups to unveil the microscopic origin of high critical temperature superconductivity which has resisted theoretical investigations for twenty years. Such a breakthrough may help designing room temperature superconductors opening the path to revolutionary applications such as the storage and transport of electricity without loss.
The equation of state of ultracold Bose and Fermi gases : a few examples, S. Nascimbène, N. Navon, F. Chevy, C. Salomon, arXiv:1006.4052, to be published in New Journal of Physics.