A Fermi gas at infinite scattering length (unitary Fermi gas) has been realized in ultracold atom experiments and attracted considerable interests across many subfields in physics because of its strong interaction, scale invariance, and universality. I will start with introducing an epsilon expansion technique, which provides reasonable estimates of key quantities of the unitary Fermi gas [1]. The epsilon expansion also reveals the fact that the unitary Fermi gas exists only in 3D and becomes trivial in other dimensions. However, I will show that analogs of the unitary Fermi gas (and associated BCS-BEC crossover physics) exist in "mixed dimensions" [2,3] and 4-body interaction in 1D, where I discuss rich many-body physics appears [4-5]. This study considerably extends our perspectives on the universal few-body and many-body physics and hopefully opens up very rich new research areas.
This talk is based on the following references partially in collaborations with D. T. Son, S. Tan, and the experimental group at Florence:
[1] "Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories" [arXiv:1004.3597]
[2] "Universal Fermi gases in mixed dimensions" Phys. Rev. Lett. 101, 170401 (2008) [arXiv:0806.2668]
[3] "Scattering in mixed dimensions with ultracold gases" Phys. Rev. Lett. 104, 153202 (2010) [arXiv:1002.0114]
[4] "Phases of a bilayer Fermi gas" Phys. Rev. A 82, 011605(R) (2010) [arXiv:0906.4584]
[5] "Universal four-component Fermi gas in one dimension" Phys. Rev. A (2010) [arXiv:0908.2159]