Now they went to test it, which they did by supercooling potassium atoms while using lasers to force them into one place. (Conveniently you can also use lasers for refrigeration though I'm not sure if they did.) Then they switched the lasers to describe a big 2D standing wave which the potassium atoms spread out into, forming a square grid. These are called "optical lattices"; they're difficult to work with because you don't have anything small enough to really poke at individual atoms and even if you did you'd have to deal with how the lasers are blasting your poker left and right... so, you just have to kind of throw your hands up, "I am not going to care about any of these individual atoms." However, you get some nice bulk properties: for an easy example, if you just turn off the lasers and let stuff drift and then image it, they all basically started from the same place and drifted according to their velocity which is proportional to their momentum, so you can get an image of |ψ[p]|², the momentum-space distribution of the wavefunctions of the individual atoms. So that's cool. But basically you have this tiny little dot of well-arranged well-controlled particles, but you can only do bulk operations on them (including e.g. bulk entanglements by bringing pairs of rows closer together by messing with the lattice and cool stuff like that).
While I'm not clear what the theoretical predictions were, exactly, apparently when they pushed the system into the first temperature regime described above they discovered whatever their theoretical model predicted. Hooray! This has given them some small confidence that maybe their theoretical model is a plausible step forward for understanding high-T superconductivity.