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We investigate the stability of a three spin state mixture of ultracoldfermionic $^6$Li atoms over a range of magnetic fields encompassing threeFeshbach resonances. For most field values, we attribute decay of the atomicpopulation to three-body processes involving one atom from each spin state andfind that the three-body loss coefficient varies by over four orders ofmagnitude. We observe high stability when at least two of the three scatteringlengths are small, rapid loss near the Feshbach resonances, and two unexpectedresonant loss features. At our highest fields, where all pairwise scatteringlengths are approaching $a_t = -2140 a_0$, we measure a three-body losscoefficient $L_3 \simeq 5\times 10^{-22} \mathrm{cm}^6/\mathrm{s}$ and a trendtoward lower decay rates for higher fields indicating that future studies ofcolor superfluidity and trion formation in a SU(3) symmetric Fermi gas may befeasible.

Three-body recombination in a three-state Fermi gas with widely tunable interactions