Density Profiles of Strongly Interacting Trapped Fermi Gases

We study density profiles in trapped fermionic gases, near Feshbach resonances, at all $T\le T_c$ and in the near Bose-Einstein condensation and unitary regimes. For the latter, we characterize and quantify the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.

Figure 1

Density profile and its decomposition in the near-BEC limit ($1/k_{F}a=3.0$) at $T/T_c=0.5$. Shown are the actual plots on the left for the total $n(r)$, the noncondensed pairs $n_{\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r}}$, and the condensate $n_s$. The right panel shows how these two (indicated by the shaded areas from top to bottom) add together to give $n(r)$.

Figure 2

Density profiles and their decompositions for the unitary case ($1/k_{F}a=0$) at $T=0.75T_c$. The upper and lower panels correspond to Eqs. (6) and Eqs. (4), respectively. On the left are shown the actual plots for the total, the noncondensed pairs, condensate, and fermion density. Shown on the right is how the last three, as indicated by the shaded areas from top to bottom of each panel, add up to the local density $n(r)$.

Figure 3

Temperature dependence of (a) experimental one-dimensional spatial profiles (circles) and TF fit (line) from Ref. 12, (b) TF fits (line) to theory both at $T\approx 0.7T_c\approx 0.19T_F$ (circles), and (c) overlay of experimental (circles) and theoretical (line) profiles, as well as (d) relative rms deviations (${\chi }^2$) associated with these fits to theory at unitarity. The circles in (b) are shown as the line in (c). The profiles have been normalized so that $N=\int \overline{n}(x)dx=1$, and we set $R_{\mathrm{T}\mathrm{F}}=100\mu \mathrm{m}$ in order to overlay the two curves. ${\chi }^2$ reaches a maximum around $T=0.19T_F$.