Understanding the superfluid phase diagram in trapped Fermi gases

Trapped ultracold Fermi gases provide a system that can be tuned between the BCS and Bose-Einstein condensation regimes by means of a magnetic-field Feshbach resonance. Condensation of fermionic atom pairs in a ${}^{40}\mathrm{K}$ gas was demonstrated experimentally by a sweep technique that pairwise projects fermionic atoms onto molecules. In this paper, we examine previous data obtained with this technique that probed the phase boundary in the temperature-magnetic field plane. Comparison of the ${}^{40}\mathrm{K}$ data to a theoretically computed phase diagram demonstrates good agreement between the two.

Figure 1

(Color online) (a) Physical temperature $T∕T_F^0$ (dashed curves), effective temperature $(T∕T_F{)}^0$ (solid curves) at the superfluid transition (black curves) and $N_s∕N=0.01$ (red curves). (b) $\mu \left(T_c\right)$ (black curve) and $\Delta \left(T_c\right)$ (blue curve) at the trap center as functions of $1∕k_F^{0}a$. In (a), the solid lines also represent approximately $S∕N_a{k}_B$ $(\propto T^0)$, where $N_a$ is the total number of atoms of both spins. $(T∕T_F{)}^0$ is the temperature measured in the noninteracting Fermi gas limit.

Figure 2

(Color online) Entropy per particle $S∕N_a{k}_B$ as a function of physical temperature $T∕T_F^0$ for $1∕k_F^{0}a=-\infty$ (black), $0$ (red, dashed), and $1∕2$ (blue, dot-dashed line), representing the ideal Fermi gas, unitary, and strongly interacting near-BEC cases, respectively.

Figure 3

(Color) Phase diagram of ${}^{40}\mathrm{K}$. A contour plot of the measured condensate fraction $N_0∕N$ as a function of $1∕k_F^{0}a$ and effective temperature $(T∕T_F{)}^0$ is compared with theoretically calculated contour lines at $N_s∕N=0$ (at the superfluid transition, black curve) and 0.01 (red curve). The experimental data have an overall systematic uncertainty of approximately 0.1 in $1∕k_F^{0}a$. The overall trend of the experimental contour of $N_0∕N=0.01$ and the theoretical line for $N_s∕N=0.01$ are in good agreement. The dashed line represents the naive BCS result $T_c∕T_F^0\approx 0.615e^{\pi ∕2k_F^{0}a}$. Here all temperatures are measured in the Fermi gas regime.

Figure 4

(Color) The theoretically computed equilibrium phase diagram and contour plot of the superfluid density $N_s∕N$ as a function of $(T∕T_F{)}^0$ and $1∕k_F^{0}a$.