Measurement of the Interaction Energy near a Feshbach Resonance in a ${}^6\mathrm{L}\mathrm{i}$ Fermi Gas

We investigate the strongly interacting regime in an optically trapped ${}^6\mathrm{L}\mathrm{i}$ Fermi mixture near a Feshbach resonance. The resonance is found at $800(40)\mathrm{G}$ in good agreement with theory. Anisotropic expansion of the gas is interpreted by collisional hydrodynamics. We observe an unexpected and large shift (80 G) between the resonance peak and both the maximum of atom loss and the change of sign of the interaction energy.

Figure 1

Predicted scattering length versus magnetic field in ${}^6\mathrm{L}\mathrm{i}$ $|F,m_F⟩=|1/2,1/2⟩,|1/2,-1/2⟩$ mixture.

Figure 2

Left: Geometry of the trapped atomic cloud (center) and expansion images without magnetic field (a) ($B=0$), and with magnetic field (b) ($B\ne 0$). Right: Corresponding Gaussian sizes of the expanded clouds along $x$ (squares) and $y$ (open circles) versus magnetic field. (a) Time of flight images after $650\mu \mathrm{s}$ expansion with $B=0$. (b) Images after $400\mu \mathrm{s}$ expansion with $B\ne 0$ and $250\mu \mathrm{s}$ with $B=0$. Images shown on the left are for $B=900\mathrm{G}$.

Figure 3

(a),(b) Gaussian sizes along $x$ and $y$ versus magnetic field. The detection conditions and symbols are the same as in Fig. 2. (a) Expansion with $B=0$, (b) expansion with $B\ne 0$, (c) number of detected atoms versus magnetic field. Open triangles and black diamonds correspond to graphs (a) and (b), respectively. Line L1 corresponds to the maximum of loss, and L2 to the resonance position.

Figure 4

Ratio of the interaction to kinetic energy versus magnetic field. Open squares: samples prepared above resonance as in Fig. 2. Crosses: average of three sets of data, recorded in conditions of Fig. 3. Solid/dashed curve: mean field calculation for $7\times {10}^4$ atoms and kinetic energy $E_{\mathrm{k}\mathrm{i}\mathrm{n}}/k_B=5.25\mu \mathrm{K}$. The gray area indicates the region of losses.