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Résumé |
Ultracold atomic Fermi gases have been widely studied from both theoretical and experimental point of view during the last decades. In the low density regime, the two-body interaction between the constituents is well described by the leading order of the $s$-wave scattering channel and can be fine tuned from weak to strong coupling by applying an external magnetic field. Such systems are remarkable laboratories to test and design many-body theories. In particular, the low density limit of strong coupling for which the $s$-wave scattering length $a_s$ is infinite, namely the unitary gas limit, has recently received a special and growing interest in nuclear physics due to the presence of anomalously large scattering length $a_s \sim -20~\text{fm}^{-1}$. Especially the perturbation expansion of observables fails for density $\rho \gtrsim 10^{-7} \rho_0$ where $\rho_0$ is the saturation density. Resummation techniques have been investigated in Effective Field Theory (EFT) framework for infinite matter by summing up all orders in perturbation of a certain class of Feynman diagrams to describe properties of strongly interacting Fermi systems. These resummations result in compact expressions of the energy as a function of low energy constants and density.
The aim of this work is to propose a non-empirical density functional theory for ultracold atoms based on resummation techniques keeping the information on the interaction. In this presentation, I will first introduce resummation theory for ultracold atoms and present simplified density functionals obtained describing remarkably well the thermodynamic properties of Fermi gas from small scattering length to unitarity. Then I will discuss the possibility to use resummation for the self-energy that encodes the quasi-particle properties. I will show, as an illustration, the resummed effective mass and effective potential extracted from the self-energy and discuss the link with Landau Fermi liquid theory and perspectives for density functional approaches. |
