Chromium dipolar Fermi sea

We report on the production of a degenerate Fermi gas of ${}^{53}\mathrm{Cr}$ atoms, polarized in the state $F=9/2, m_F=-9/2$, by sympathetic cooling with bosonic $S=3,m_S=-3 {}^{52}\mathrm{Cr}$ atoms. We load in an optical dipole trap $3\times {10}^4{}^{53}\mathrm{Cr}$ atoms with ${10}^6 {}^{52}\mathrm{Cr}$ atoms. Despite the initial small number of fermionic atoms, we reach a final temperature of $T\simeq 0.6\times T_f$ (Fermi temperature), with up to ${10}^3 {}^{53}\mathrm{Cr}$ atoms. This surprisingly efficient evaporation stems from an interisotope scattering length $|a_{BF}|=80(\pm 10)a_B$ (Bohr radius) which is small enough to reduce evaporative losses of the fermionic isotope, but large enough to assure thermalization.

Figure 1

Inelastic interspecies collisions in the ODT. The lifetime of ${}^{53}\mathrm{Cr}$ atoms in the ODT dramatically drops when ${}^{52}\mathrm{Cr}$ atoms are loaded starting at $t=0$. This sets a tight constraint to optimize loading before sympathetic cooling. Solid lines are fit to the data, using exponential functions. Error bars show statistical uncertainties. Inset: chromium energy levels of interest.

Figure 2

Time evolution of ${}^{52}\mathrm{Cr}$ temperature $\left(T_B\right)$ and atom number of both isotopes during evaporation. The crossed dipole trap is fully loaded at $t=7$ s. The evaporation ends at $t=12$ s. Inset: in situ absorption image of a degenerate fermionic ${}^{53}\mathrm{Cr}$ cloud of ${10}^3$ atoms, with corresponding integrated optical depth.

Figure 3

Comparison between the two isotopes during evaporation. Left: Atom numbers showing the smaller losses for fermions. The (red) curve is the prediction from Eq. (2); the straight (blue) line assumes constant ratio between atom numbers. Right: Temperatures. The temperature of the fermion remains about $20\%$ higher than that of the boson during the whole sequence. The straight (blue) line corresponds to identical temperatures.

Figure 4

Experimental measurements of the ratio of the boson-boson and interisotope cross sections obtained using Eq. (2), with $t_1=10$ s (see text). The error bar shows the systematic uncertainty associated with ${\eta }_{B,F}$, which dominates over statistical uncertainties. Inset: scattering lengths of Cr, including $a_{52\text{–}53}$ (this work). The solid line is the predicted scattering length using mass scaling of semiclassical phase [18].