Three-Body Recombination in a Three-State Fermi Gas with Widely Tunable Interactions

We investigate the stability of a three spin state mixture of ultracold fermionic ${}^6\mathrm{Li}$ atoms over a range of magnetic fields encompassing three Feshbach resonances. For most field values, we attribute decay of the atomic population to three-body processes involving one atom from each spin state and find that the three-body loss coefficient varies by over 4 orders of magnitude. We observe high stability when at least two of the three scattering lengths are small, rapid loss near the Feshbach resonances, and two unexpected resonant loss features. At our highest fields, where all pairwise scattering lengths are approaching $a_t=-2140a_0$, we measure a three-body loss coefficient $L_3\simeq 5\times {10}^{-22}{\mathrm{cm}}^6/\mathrm{s}$ and a trend toward lower decay rates for higher fields indicating that future studies of color superfluidity and trion formation in a SU(3) symmetric Fermi gas may be feasible.

Figure 1

The $s$-wave scattering lengths as a function of magnetic field for interactions between the three lowest energy hyperfine ground states of ${}^6\mathrm{Li}$ ($|1⟩$, $|2⟩$, and $|3⟩$) [15]. Feshbach resonances occur at 690, 811, and 834 G.

Figure 2

The population in states $|1⟩$, $|2⟩$ and $|3⟩$ measured by absorption imaging in the Paschen-Back regime at a bias field of 568 G [23]. A ${\sigma }^{-}$ polarized probe beam drives $m_j=-\frac{1}{2}\to m_{j^{\prime }}=-\frac{3}{2}$ transitions which, due to the hyperfine interaction in the ground state, are spectroscopically resolvable. (Top right) The on-resonance absorption images show the density profile for the three states following a $900\mu \mathrm{s}$ time-of-flight expansion. (Bottom right) The total absorption vs probe detuning (relative to the $|f=\frac{1}{2},m_f=-\frac{1}{2}⟩\to |f^{\prime }=\frac{3}{2},m_{f^{\prime }}=-\frac{3}{2}⟩$ transition frequency in zero field).

Figure 3

(a) Number remaining in each of the three spin states after spending 201 ms at the field of interest $B$ (normalized to the number remaining after spending 1 ms at $B$). (b) Magnetic field dependence of decay in individual two-state mixtures. ◆ (●) indicates the normalized number remaining in state $|2⟩$ ($|3⟩$) of a $|2⟩\mathrm{\text{−}}|3⟩$ ($|1⟩\mathrm{\text{−}}|3⟩$) mixture after 201 ms. The thick lines guide the eye. The representative error bars indicate the standard deviation in the mean. Absorption images are taken at 953 G to ensure that any weakly bound molecules which remain trapped are dissociated and measured.

Figure 4

Three-body loss rate coefficient, $L_3$, at various fields.