Spectroscopy of Superfluid Pairing in Atomic Fermi Gases

We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state.

Figure 1

Diagrams contributing to the density response function and the spin susceptibility; ${\chi }_{\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}}$ accounts for particle-hole excitations, while the diagrams in ${\chi }_{\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{l}}$ describe collective sound excitations.

Figure 2

Spin structure factor $S_{\mathrm{S}}(\omega )$ in units $\hslash n_{\mathrm{F}}/E_{\mathrm{F}}$ for different scattering lengths $1/(a_{\mathrm{F}}{k}_{\mathrm{F}})=-0.5,0,0.5,1,1.5$. The spin structure is quenched below the spin gap $\omega <{\Delta }_{\mathrm{S}}$ and exhibits a characteristic singularity in the BCS limit.

Figure 3

Left: sound velocity $c_s$ in the BEC-BCS crossover in units $v_{\mathrm{F}}/\sqrt{3}$. The dashed line is the Bogoliubov sound velocity. Right: structure factor $S_{\mathrm{C}}(\omega )$ of weakly interacting fermions and bosons above the superfluid transition temperature $T={ϵ}_{\mathrm{F}}/2>T_c$ and $k=\sqrt{3}{k}_{\mathrm{F}}/40$. The gray line denotes the peak of the sound mode below the superfluid transition.