Recent breakthroughs in the creation of ultra-cold atoms in the laboratory have ushered in major changes in physical science. These enormous changes in the coldest temperatures available in the laboratory mean that many novel experiments are possible. There is unprecedented control of interaction, geometry and purity in these novel systems, meaning that quantum many-body theory is now facing severe challenges in quantitatively understanding these new results. Here, we discuss some of the new experiments on strongly interacting fermions and recently developed theoretical techniques that are proving successful today in understanding the experimental results. These are: (a) Infinite order perturbation theory [1,2,3]; (b) High temperature quantum cluster expansion [4,5]; (c) Exact solutions for one-dimensional and few-particle systems [6]; (d) Asymptotically exact relations for structure factor [7,8].

References

[1] Hui Hu, Xia-Ji Liu, and Peter D. Drummond, Europhys. Lett. 74, 574 (2006).
[2] Hui Hu, Peter D. Drummond, and Xia-Ji Liu, Nature Phys. 3, 469 (2007).
[3] Hui Hu, Xia-Ji Liu, and Peter D. Drummond, arXiv:1001.2085; to appear in New J. Physics
[4] Xia-Ji Liu, Hui Hu, and Peter D. Drummond, Phys. Rev. Lett. 102, 160401 (2009).
[5] Hui Hu, Xia-Ji Liu, Peter D. Drummond, and Hui Dong, Phys. Rev. Lett. 104, 240407 (2010).
[6] Hui Hu, Xia-Ji Liu, and Peter D. Drummond, Phys. Rev. Lett. 98, 070403 (2007).
[7] Hui Hu, Xia-Ji Liu, and Peter D. Drummond, arXiv:1003.3511; to appear in Europhys. Lett.
[8] C. J. Vale et al., arXiv:1001.3200v1.