Observation of Anomalous Spin Segregation in a Trapped Fermi Gas

We report the observation of spin segregation, i.e., time-dependent separation of the spin density profiles of two spin states, in a trapped, coherently prepared Fermi gas of ${}^6\mathrm{Li}$ with a magnetically tunable scattering length $a_{12}$ close to zero. For $|a_{12}|\simeq 5\mathrm{bohr}$, as the cloud profiles evolve, the measured difference in the densities at the cloud center increases in 200 ms from 0 to $\simeq 60\%$ of the initial mean density and changes sign with $a_{12}$. The data are in disagreement in both amplitude and temporal evolution with a spin-wave theory for a Fermi gas. In contrast, for a Bose gas, an analogous theory has successfully described previous observations of spin segregation. The observed segregated atomic density profiles are far from equilibrium, yet they persist for $\simeq 5\mathrm{s}$, long compared to the axial trapping period of 6.9 ms. We find the zero crossing in $a_{12}=0$, where spin segregation ceases, at $527.5\pm 0.2\mathrm{G}$.

Figure 1

Absorption images (states 1 and 2) taken at 200 ms after the rf pulse for 526.2 (scattering length $a_{12}<0$) and 528.8 G ($a_{12}>0$). Each image is 1.2 mm in the horizontal direction.

Figure 2

(a) Axial atomic density profiles $n_1$ and $n_2$ (integrated over transverse directions) versus time relative to the end of the rf pulse for different magnetic fields and scattering lengths ($B$, $a_{12}$). $a_{12}$ is estimated with $a_{12}(B)=\acute{a}(B-B_0)$, where $\acute{a}=3.5a_0/\mathrm{G}$ [13, 14] and $B_0=527.5\mathrm{G}$ is the zero crossing measured in the experiments. Note that different graphs have different time scales; (b) $n_2-n_1$ at 200 ms for $B=526.2\mathrm{G}$ in units of $n_0=(n_{10}+n_{20})/2$. Here $n_{i0}$ is the spin density for state $i=1,2$ at the trap center before spin segregation occurs. The solid red curve is the prediction at maximum segregation multiplied by a factor of 200, which oscillates in time with a period of $\simeq 7\mathrm{ms}$, inconsistent with our observations; (c) $n_2-n_1$ at the trap center versus time for $B=526.2\mathrm{G}$. The spin density relaxes back to equilibrium at 10 s.

Figure 3

Axial atomic density profiles at 200 ms after coherence is created by an rf pulse, for different magnetic fields. The zero crossing point in the scattering length is determined by observing the change in the sign of the difference in the spin densities as the magnetic field is varied.