Final Report Summary - FERLODIM (Atomic Fermi Gases in Lower Dimensions) The FERLODIM project belongs to the field of quantum gases and many-body physics. When cooling a gas to ultra-low temperatures, its properties can no longer be described by classical physics. The gas properties are governed by Quantum Mechanics and spectacular collective properties such as Bose-Einstein condensation and superfluidity may occur when quantum statistics and interactions come into play. For a gas of bosons (particles with integer spin) confined in a box, Bose-Einstein condensation occurs below a certain critical temperature and corresponds to a macroscopic occupation of a single quantum state of the box. In 3 dimensions, this state is a superfluid state. On the other hand for fermions (particles with half-integer spin), the Pauli exclusion principle forbids Bose Einstein condensation for a single spin state. As shown by Bardeen Cooper and Schrieffer more than 50 years ago, superfluidity is recovered when fermions with two spin states and attractive interactions are considered. The field of quantum gases is enjoying a very rapid development thanks to the progress in precise control of atoms and molecules using cooling and trapping techniques. In FERLODIM, ultracold gases have served as model systems that, on the one hand, enabled us to test with high precision advanced theories of quantum correlated matter and, on the other hand, to develop totally new models. Very often these theories have been proposed to describe properties of condensed matter but have failed to be tested in solid-state systems because of their intrinsic complexity. With a new and powerful detection technique, we have studied these quantum correlated systems with a new twist.In the last 5 years, our research group and a few others worldwide, have been able to establish for the first time a link between two types of superfluidity that at first sight appear very different; superfluidity of a Bose-Einstein condensate on one side, and superfluidity of Cooper-paired fermions on the other side [See for instance, 1-3]. This question was raised more than 30 years ago by T. Leggett and P. Nozières which proposed that the two phenomena were two sides of a unified theory called ``BEC-BCS crossover". By progressively increasing the attraction strength between fermions, we have explored this crossover between superfluidity induced by weak attraction and described by the Bardeen-Cooper-Schrieffer (BCS) theory and the Bose-Einstein condensation (BEC) of fermion pairs when the attraction between fermions is large. In between these two regimes the gas is strongly correlated and notoriously difficult to tackle theoretically because of quantum correlations.In FERLODIM, our understanding of strongly correlated Fermi (and Bose) quantum systems using ultracold atoms has followed an integrated approach that combines experiment and theory within our group and in collaboration with other researchers worldwide. We have developed two experimental set-ups, the first one employing lithium 6 atoms (fermions) cooled sympathetically by lithium 7 bosons, and the second one, employing lithium 6 and potassium 40, is dedicated to the study of mixtures of Fermi gases.In a first major achievement, we have developed a new and powerful method to measure the equation of state of homogeneous quantum gases and applied it to a variety of new situations, strongly correlated Fermi and Bose gases and spin polarized Fermi gases below and above the superfluid transition. This method has already had a large impact and shed new light on the link between cold atoms and condensed matter systems, a truly cross-disciplinary development. Second, our group has made seminal theoretical analysis of the properties of quantum gases in direct connection with experiments in-house and elsewhere, or as new proposals for future experiments. Key examples include Fermi polarons, spin dynamics, fundamental relations in unitary Bose and Fermi gases, matter-wave Anderson localization with dilute scatterers, and Kondo correlated states in cold gases. Third, we have successfully made a new laser technology development, the realization of a high power solid-state laser in the red part of the spectrum with one order of magnitude gain in output power over previously available systems. Discussions have been engaged with companies to investigate future commercial applications of this laser. Fourth, we have constructed a new quantum gas machine devoted to the study of mixtures of fermions that has excellent properties in terms of atom number and experiment stability. In this endeavour we have proposed and implemented a new and very efficient laser cooling scheme that overcomes fundamental cooling limitations set by the hyperfine structure of some alkalis atoms. Finally, with a total of 27 students, postdocs, and permanent members (from 9 different countries) directly involved in the FERLODIM project over its 5 years lifetime, and with a dozen of external collaborators, the activity and international visibility of the group has significantly been enhanced by this ERC Advanced Grant. This is testified by the number of published papers in high visibility journals (33), invited talks in international (69) and national (7) conferences, and awards (4). Papers acknowledging the ERC Ferlodim support include 1 Nature, 1 Science, 8 PRL, 4 EPL, 10 PRA, and 7 in other journals.
