Abstract
Recently, ultra-cold atoms have established a very fruitful connection with condensed matter physics, nuclear physics, astrophysics, and high energy physics on many-body problems in strongly correlated systems. Starting from the pioneering work of Popov and Eagles in the 1970s [1], the connection between superfluidity in a fermionic system with attractive interaction and superfluidity of bosonic pairs of fermions has been the subject of intense theoretical activity (See for instance [2, 3] and other contributions in this book). While the two limiting cases, weakly attractive Fermi gas and weakly repulsive Bose gas are well described by mean field theories, the so-called BEC–BCS crossover region where the gas is strongly correlated poses a challenging theoretical problem. A flurry of theoretical works (see for instance [2, 4, 5, 6, 7, 8, 9]) have been developed in order to address the properties of this seemingly simple many-body system of a fermionic species with two spin states interacting with purely s-wave contact potential, but with tunable strength.
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