Quantitative Comparison between Theoretical Predictions and Experimental Results for the BCS-BEC Crossover

Theoretical predictions for the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of ${}^{\mathrm{6}}\mathrm{L}\mathrm{i}$. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.

Figure 1

Comparison between experimental and theoretical axial density profiles. Experimental data from Ref. 17 (dots) are shown for three different values of the magnetic field $B$ tuning the FF resonance. Theoretical results at $T=0$ obtained by our theory (solid lines) and by BCS mean field (dashed lines) are shown for the corresponding couplings $(k_F{a}_F{)}^{-1}$ given in the text. The upper (lower) panel refers to the estimated number of atoms $N=4\times {10}^5$ ($N=2.3\times {10}^5$).

Figure 2

Comparison between experimental (dots) and theoretical (triangles) normalized root-mean square axial radius across the crossover regime. Experimental data are taken from Ref. 17. The values of $(k_F{a}_F{)}^{-1}$ and of the noninteracting root-mean square axial radius used also for the experimental data are obtained with $N=2.3\times {10}^5$.

Figure 3

Comparison between experimental results for the axial density profile (dots) and the predictions of Bogoliubov theory, obtained with $a_B/a_F=2$ (dash-dotted line), $a_B/a_F=0.75$ (dashed line), and $a_B/a_F=0.6$ (solid line). Experimental data were obtained in Ref. 17 deep in the BEC region, corresponding to $(k_F{a}_F{)}^{-1}=5.44$ when $N=2.3\times {10}^5$.