Collisional Stability of a Three-Component Degenerate Fermi Gas

We report on the creation of a degenerate Fermi gas consisting of a balanced mixture of atoms in three different hyperfine states of ${}^6\mathrm{Li}$. This new system consists of three distinguishable fermions with different and tunable interparticle scattering lengths $a_{12}$, $a_{13}$, and $a_{23}$. We are able to prepare samples containing $5\times {10}^4$ atoms in each state at a temperature of about 215 nK, which corresponds to $T/T_F\approx 0.37$. We investigated the collisional stability of the gas for magnetic fields between 0 and 600 G and found a prominent loss feature at 130 G. From lifetime measurements, we determined three-body loss coefficients, which vary over nearly 3 orders of magnitude.

Figure 1

Zeeman hyperfine levels of ${}^6\mathrm{Li}$ in the electronic ground state. Transitions between adjacent hyperfine states can be driven with external rf fields.

Figure 2

(a) Magnetic field dependence of the remaining fraction of atoms after holding a three-state mixture for 250 ms. (b) Result for a two-state mixture under the same experimental conditions. The enhanced trap loss at fields larger than 600 G is due to high inelastic collision rates close to the two-body Feshbach resonances, which also causes loss in the three-component mixture. For magnetic fields larger 600 G, molecules are formed in the $|1⟩-|3⟩$ channel which are not detected when ramping back for imaging. (c) Two-body scattering lengths for all spin-state combinations [33] ($a_{ii}=0$ for symmetry reasons).

Figure 3

Evolution of (a) atom number and (b) temperature of atoms in state $|2⟩$ over five seconds at 300 G. $\overline{T}$ denotes an effective temperature deduced from a Gaussian fit to the cloud after time of flight. Each data point is a mean value of three independent measurements taken in random order. The solid line is a fit to the data, applying the method described in the text.

Figure 4

Three-body loss coefficient $K_3$ vs magnetic field.