Pairing Fluctuations in Trapped Fermi Gases

We examine the contribution of pairing fluctuations to the superfluid order parameter for harmonically trapped atomic Fermi gases in the BCS regime. In the limit of small systems we consider, both analytically and numerically, their space and temperature dependence. We predict a parity effect, i.e., that pairing fluctuations show a maximum or a minimum at the center of the trap, depending on the value of the last occupied shell being even or odd. We propose to detect pairing fluctuations by measuring the density-density correlation function after a ballistic expansion of the gas.

Figure 1

Lowest eigenvector ${\chi }_0(r)$ vs $r$: numerical diagonalization (solid line), analytical solution (10) (dot-dashed line), and Thomas-Fermi approximation (dashed line). The inset shows $\langle |\Delta (r=0){|}^2{\rangle }^{1/2}$ vs temperature: quartic (solid line) and quadratic (dashed line) approximation of the effective action, and mean-field solution (dotted line). The units are indicated on the figure axis.

Figure 2

Lowest eigenvalue ${\alpha }_0(T)$ vs temperature as calculated numerically (×) and analytically via Eq. (11) (solid line). The inset shows the lowest eigenvalues ${\alpha }_{\nu }$ vs $\nu$, evaluated at $T\sim T_c$. The units are indicated on the figure axis.