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In cold atom experiments one can adjust at will the atomic interaction strength: with a simple application of a magnetic field, one can in principle tune the s-wave scattering length from minus infinity to plus infinity. For spin 1/2 fermions this has in particular led to the first observation of the crossover between a BCS state of Cooper pairs and a Bose-Einstein Condensate of dimers [1,2].
In this theoretical talk, we shall focus on the particularly fascinating case of an infinite scattering length. For spin 1/2 fermions, this leads to the so-called unitary gas, which was recently the subject of precise equation-of-state measurements/numerical calculations [3,4]. We shall review the intriguing physical consequences of scaling invariance of this maximally interacting gas, and make the link with Efimov physics:
- mathematical representation by the Wigner-Bethe-Peierls (or zero-range) model  - dynamical consequences of the scaling invariant, and SO(2,1) hidden symmetry in a trap  - does the unitary gas really exist ? The threat of a generalized Efimov effect  - effect of mass imbalance between the two components: the single impurity problem, three-body  and four-body  Efimov effects - what about the mysterious ”unitary Bose gas” ?