It would be really helpful if somebody could describe what does one mean by a BEC-BCS Crossover. I was going through articles available on the topic, but I was unable to grasp the gist of the topic.
In the context of ultracold Fermi gases, a BEC-BCS crossover means that by tuning the interaction strength (the s-wave scattering length), one goes from a BEC state to a BCS state without encountering a phase transition (thus the word "crossover").
It is also useful to know that the BEC state is a Bose-Einstein condensate of two-atom molecules, while the BCS state is made up of pair of atoms. The different between the pairs and the molecules is that the molecules are localized in the real (position) space, whereas the BCS pairs are made of two particles with opposite momenta. Thus, the BCS pairs are large (much larger than the inter-particle spacing), whereas the BEC molecules are small.