Progress towards the fermion Hubbard model (beloved in the strongly correlated electron community) has been slower.
Cooling fermionic atoms is much more difficult.
There is a recent PRL which gives some indication of where things are at.Observation of 2D Fermionic Mott Insulators of K40 with Single-Site Resolution
Lawrence W. Cheuk, Matthew A. Nichols, Katherine R. Lawrence, Melih Okan, Hao Zhang, and Martin W. Zwierlein
The figure below shows the measured local magnetic moment as a function of temperature. The upper curve is at half filling and the bottom for a strongly doped system. The solid lines are theoretical curves obtained from high temperature series expansions.
The temperature is scaled by the hopping integral t in the Hubbard model.
The authors note they have reached entropies as low as k_B.
Although this is significant progress it should be noted that these are still very high temperatures from a solid state physics perspective. For the high T_c cuprate superconductors, these temperatures correspond to tens of thousands of Kelvin, two orders of magnitude about the superconducting transition temperature.
On a more promising note, there is interesting physics to access in the Hubbard model at temperatures of order of some fraction of t and at entropies of order k_B . ln(2).
These are the characteristic scales of the bad metal regime.
A particularly interesting experiment would be to measure the viscosity in this regime and see whether it violates the conjectured quantum limits.
I thank my UQ colleague, Matt Davis for stimulating my interest in these issues.
Update. August 1, 2016
Thierry Giamarchi has a helpful commentary at the Journal Club for Condensed Matter Physics on two recent preprints that report similar experiments from two other groups.