As I see it ultracold atomic gases and solid-state materials have complementary strengths and weaknesses for investigating emergent quantum many-body phenomena. Solid state materials are much easier to bring to spatially uniform thermal equilibrium, achieve temperatures much less than characteristic temperatures (such as the Fermi temperature), and perform high precision thermometry. On the other hand it is hard to drive solid state systems far from equilibrium, to investigate non-equilibrium phenomena such as turbulent charge flows, and the time scales for relaxation to equilibrium are often too fast to be observed.
In contrast, ultra-cold atomic gases make it is much easier to access non-equilibrium states, and image them and their time evolution. The two platforms are also complementary in the access they provide to tune-ability, control and design. Solid state systems can be tuned considerably by temperature, pressure, magnetic field, electric field, and chemical substitution. However, sometimes it is hard to know how these variations produce changes in the underlying microscopic interactions between the constituent particles. In contrast, some of the underlying interatomic interactions in ultracold atom systems can be readily tuned from weak to strong in a precise and the known manner. However, a major challenge remains to expand the repertoire of possible tune able interactions, particularly to include some of the more common interactions found in solid state systems (e.g., the coupling of orbital motion of fermions to a magnetic field and the Heisenberg antiferromagnetic spin interaction in Mott insulators).
Here a few experiments that I would particularly like to see done and may be "relatively straight-forward", i.e, feasible in the next few years. Of particular interest would be observing these phenomena in fermionic atom systems in which one can tune the strength of the interactions, observe the BEC-BCS crossover, and universal behaviour associated with scattering close to unitarity.
Probing Thermoelectric transport with cold atoms
Quantum oscillations in ultracold Fermi gases: Realizations with rotating gases or artificial gauge fields
Charles Grenier, Corinna Kollath, Antoine Georges
The "Higgs boson"!
Visibility of the amplitude (Higgs) mode in condensed matter
Daniel Podolsky, Assa Auerbach, and Daniel P. Arovas
The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition
This then connects to
Conductivity of hard core bosons: A paradigm of a bad metal
by Lindner and Auerbach
An earlier post discussed this paper, suggesting calculation of the thermopower.
Observation of an d-wave pseudogaps. For the s-wave case see
Observation of a pairing pseudogap in a two dimensional Fermi gas.