%0 Journal Article %T Turning the BEC-BCS crossover into a transition by radiation %A Y. Lemonik %A I. L. Aleiner %A B. L. Altshuler %J Physics %D 2015 %I arXiv %X We show that the Bardeen-Cooper-Schrieffer state (BCS) and the Bose-Einstein condensation (BEC) sides of the BCS-BEC crossover can be rigorously distinguished from each other by the extrema of the spectrum of the fermionic excitations. Moreover, we demonstrate that this formal distinction is realized as a non-equilibrium phase transition under radio frequency radiation. The BEC phase remains translationally invariant, whereas the BCS phase transforms into the supersolid phase. For a two-dimensional system this effect occurs at arbitrary small amplitude of the radiation field. %U http://arxiv.org/abs/1505.04820v1