Strong correlations in the normal phase of an attractive Fermi gas

The purpose of this thesis is the study of an attractive Fermi gas in the normal phase throughout the BCS-BEC crossover by means of diagrammatic approaches based on the t-matrix approximation. More specifically, the calculation is implemented by including different degrees of self-consistency in the t-matrix equations, from the non-self-consistent to the fully self-consistent (or Luttinger-Ward) approach. In the first part of the thesis, we perform a systematic and unbiased comparative study of all the five variants of the t-matrix approach with different degrees of selfconsistency considered thus far in the literature. The analysis is performed by calculating several thermodynamic and dynamical quantities of the spin-balanced Fermi gas in the normal phase within all the approaches. We also compare these results with the available quantum Monte Carlo (QMC), diagrammatic Monte Carlo (DMC) and experimental data. In the comparison, the fully self-consistent t-matrix approach turns up to be the best to describe thermodynamic quantities, however for dynamical quantities partially or non-self-consistent approaches appear to work better. In the second part of the thesis, we investigate pairing correlations in the normal phase of the spin-balanced system within the fully self-consistent t-matrix approach. We first calculate the pair correlation function g↑↓(ρ) and the pair coherence length ξpair for various couplings and temperatures. We then develop a new approach, based on the two-body Green’s function formalism, to calculate the number of preformed pairs in the normal phase. The approach is used to describe the experimental data on this quantity by the group of Prof. Denschlag in Ulm. In order to compare our calculation with the experiment, the fully self-consistent t-matrix approach is extended to consider a Fermi gas in a harmonic trapping potential. In general, very good agreement is found with experimental data. In the final part of the thesis, we present some preliminary results for the spinimbalanced Fermi gas, focusing on the temperature-coupling-polarization phase diagram and on T = 0 and finite T thermodynamic quantities. In this analysis, we show that the Luttinger theorem for an imbalanced Fermi gas at T = 0 is satisfied within the fully self-consistent t-matrix approach, and we present the extension of the calculation of the pair correlation function g↑↓(ρ) to the spin-imbalanced case.