Quasiparticle dispersions and lifetimes in the normal state of the BCS-BEC crossover

We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a $T$-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a “pseudogap” energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold. We also find that, near unitarity, the quasiparticle lifetimes, estimated from the widths of the peaks in the spectral density, approach values on the order of the inverse Fermi energy. These results are consistent with the “breakdown of Fermi-liquid theory” observed in recent experiments.

Figure 1

Diagrammatic representation of the $T$-matrix approximation used in this paper [Eq. (2)].

Figure 2

Spectral density in the normal phase for various interaction strengths at temperature $T=1.1T_c$. Lighter colors correspond to higher spectral density.

Figure 3

Peak locations of the spectral density at $1/k_{F}a=0.18(T=1.1T_c)$. The solid lines show least-squares fits to the dispersion relation in Eq. (8). The broad and asymmetric nature of the peaks prevents us from determining the lower-branch dispersion in the range $1.0k_F\lesssim k\lesssim 1.25k_F$.

Figure 4

Pseudogap energy scale ${\Delta }_{-}$ (orange) and ${\Delta }_{+}$ (blue) extracted from fits of Eq. (8) to the peak locations in the spectral density $\left(T=1.1T_c\right)$.

Figure 5

Effective Fermi wave vectors $k_{L_{-}}$ (orange) and $k_{L_{+}}$ (blue) extracted from fits of Eq. (8) to the peak locations in the spectral density $\left(T=1.1T_c\right)$.

Figure 6

$A(k=k_F,E)$ at $\frac{1}{k_{F}a}=0.18(T=1.1T_c)$. The solid red line is a fit of the data to the sum of two Lorentzians. The two widths extracted from these fits provide estimates of the inverse quasiparticle lifetimes ${\tau }^{-1}$. ${\tau }^{-1}$ at other interaction strengths are plotted in Fig. 7.

Figure 7

Inverse quasiparticle lifetimes ${\tau }^{-1}$ as a function of interaction strength $\left(T=1.1T_c\right)$. The orange (blue) points are the spectral widths of the negative-energy (positive-energy) branch of the quasiparticle spectral peak at $k=k_F$.