Finite-temperature momentum distribution of a trapped Fermi gas

We present measurements of the temperature-dependent momentum distribution of a trapped Fermi gas consisting of ${}^{40}\mathrm{K}$ in the BCS to Bose-Einstein condensation crossover regime. Accompanying theoretical results based upon a simple mean-field ground state are compared to the experimental data. Nonmonotonic effects associated with temperature $T$ arise from the competition between thermal broadening and a narrowing of the distribution induced by the decrease in the excitation gap $\Delta \left(T\right)$ with increasing $T$.

Figure 1

(Color online) Evolution of the momentum distribution $N_{2D}\left(k\right)$ with the interaction strength $1∕k_F^{0}a$ from noninteracting to near-BEC cases. The two columns compare experiment (left) and theory (right). Different rows correspond to different values of ${(T∕T_F)}^0$. The lines in the experimental plots correspond to a fit to Eq. (1). The value of $k_F^0$ used to create the experimental plots was determined through experimental measurements of the particle number and trap strength, which led to systematic uncertainties in $k_F^0$ of up to 10% for these data. While the raw data are shown here, the normalization applied in Fig. 3 removes this systematic error.

Figure 2

(Color online) (a) Temperature dependence of the average excitation gap ${⟨{\Delta }^2⟩}^{1∕2}$ at $1∕k_F^{0}a=0.5$ [top (blue) curve], 0 [middle (red) curve], and $-0.5$ [bottom (black) curve]. The solid circles indicate where this effective gap coincides with the temperature. The arrows indicate the transition temperatures $T_c^0$. (b) Theoretical momentum distributions $N_{2D}\left(k\right)$ at a variety of temperatures for $1∕k_F^{0}a=0.5$.

Figure 3

(Color online) Comparison of the half width (HW) at half height as a function of ${(T∕T_F)}^0$ for different values of $1∕k_F^{0}a$ from the noninteracting (bottom curve) to near-BEC (top curve) cases between (a) experiment and (b) theory. The HW in the experimental case is normalized to eliminate dependence upon the experimental determination of $E_F^0$ (see text); this results in perfect agreement with theory in the noninteracting case [solid (black) line].