Pseudogap Pairing in Ultracold Fermi Atoms

The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer crossover in ultracold Fermi gases creates an ideal environment to enrich our knowledge of many-body systems. It is relevant to a wide range of fields from condensed matter to astrophysics. The nature of pairing in strongly interacting Fermi gases can be readily studied. This aids our understanding of related problems in high-$T_c$ superconductors, whose mechanism is still under debate due to the large interaction parameter. Here, we calculate the dynamical properties of a normal, trapped strongly correlated Fermi gas, by developing a quantum cluster expansion. Our calculations for the single-particle spectral function agree with recent rf spectroscopy measurements, and clearly demonstrate pseudogap pairing in the strongly interacting regime.

Figure 1

Contour plots of the occupied spectral intensity at crossover. The intensity $I(\omega )=A(\mathbf{k},\omega )f(\omega )k^2/(2{\pi }^2)$ increases from blue (${10}^{-3}{I}_{\max }$) to red ($I_{\max }$) in a logarithmic scale. The calculations were performed with harmonic traps at $T=0.7T_F$ and $1/(k_F{a}_s)=+1$, 0, $-1$, with a resulting fugacity at the trap center of $z\simeq 0.14$, 0.42, and 0.48, respectively.

Figure 2

Single-particle excitation spectra on the BEC side of crossover. (a)–(c) Cluster expansion predictions ($z\simeq 0.1$ and $\mu \simeq -1.08{ϵ}_F$). (d),(e) Corresponding experimental data [6]. (a) The linear-scale intensity map. Our results were convoluted with a Gaussian broadening curve of width $\sigma =0.22{ϵ}_F$, to account for the measurement resolution [6]. The black line shows upper free-atom dispersion. The red dashed line is the lower dispersion curve of molecules, obtained via fitting each fixed-$k$ energy distribution curve [in (b)] with a two Gaussian distribution. It agrees fairly well with the experimental result (white symbols). (b) Energy distribution curves for selected values of $k$. (c) The occupied density of state (DOS). Blue dashed lines show the experimental peak positions.

Figure 3

Single-particle excitation spectra of a strongly interacting Fermi gas. (a)–(c) Cluster expansion predictions ($z\simeq 6$ and $\mu \simeq 0.37{ϵ}_F$). (d),(e) Corresponding experimental data [6]. In (e), for the experimental energy distribution curves, we use a larger value of $k$ (i.e., enlarged by a factor of $5/3$) to account for a scaling discrepancy due to many-body correlations.

Figure 4

Temperature dependence of the spectral intensity at unitarity. (a)–(c) The intensity increases from blue (${10}^{-3}{I}_{\max }$) to red ($I_{\max }$) in a logarithmic scale. (d),(e) Temperature dependence of the fugacity and chemical potential at unitarity. Our leading cluster expansion appears to be applicable at $T\ge 0.4T_F$, where $z\sim 1$ or $\mu \sim 0$ [19].