I know that superfluidity and superconductivity have very distinct characteristics and have specific theories. However, it seems that in ultra-cold atomic gases these phenomena can be understood by a single model: BEC-BCS crossover. Does anyone have information on this?
A system of neutral atoms, being neutral, have no electrical conductivity. So they can not literally become superconducting.
However, a system of ultracold fermions, with weak attractive interactions, can condense into a state that is a neutral analog of the state of electrons in a superconductor. Like the electrons, these fermions form Cooper pairs, and this results in quantum coherent phenomena. This was originally achieved by the Jin group in this result, and key followups were a study in the Ketterle group which observed vortices in a spinning superfluid Fermi gas, which is analogous to the Meissner effect in electronic superconductors, and measurement of the drop in "resistance" of the neutral system by the Esslinger group.
Since ultracold fermions usually have repulsive interactions, some mechanism to make the attractions was required to make this observation possible. This turned out to be a Feshbach resonance, which is a magnetically tuned collision resonance around which the strength and sign of the effective interatomic scattering interaction varies. This meant that not only could BCS-like neutral "superconductivity" be achieved in this system, but the interaction strength could also be smoothly varied until the atoms form tightly bound molecules instead of Cooper pairs, and the appropriate theory to describe them is a BEC theory of these composite molecules. Furthermore, BEC-BCS crossover theory provides a unified framework to understand this system over the full interaction range.