Designing mixtures of ultracold atoms ​to boost $T_{c}$

​Mixtures of light and heavy atoms, with the light atom a fermion (and the heavy atom having either statistics), have a density wave ordering pattern that is analogous to the antiferromagnetic phase transition in the Hubbard model. ​For a single species mixture, the $T_{c}$ is about half the Hubbard model $T_{c}$ for the same interaction strength. As the degeneracy of the heavy species increases, the $T_{c}$ is boosted by entropic effects that scale approximately linearly in the number of species. Hence, increasing the species to $3$ or $4$ states for the heavy particle will be enough to raise $T_{c}$ above temperatures already reached for the ​three-dimensional Hubbard model on an optical lattice. \footnote{A. Hart, P. M. Duarte,T. L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D .A. Huse & R. G. Hulet, Nature 519, 211–214 (2015)}. We discuss a number of different possible mixtures which might achieve this enhanced $T_{c}$ ​and ​​allow ultracold atoms on optical lattices to study ordered quantum phases in the low-temperature regime.