Resolve the factor-of-two discrepancy in the two-body loss coefficient K_2^a

Determine the cause of the factor-of-two discrepancy between the two-body loss coefficient K_2^a inferred from 50–50 incoherent mixtures using the mixture density decay equation \dot{n}(\mathbf{r},t) = - (1/4) K_2^a n^2(\mathbf{r},t) and the K_2^a value required to fit decay data in coherently prepared energy-space spin-lattice experiments on ultracold 6Li. Ascertain whether this discrepancy arises from applying the mixture decay equation in the very weakly interacting regime or from an incorrect assumption about the incoming two-atom spin state used in deriving that equation.

Background

In the energy-space spin-lattice model, the spin-dependent inelastic loss between atoms with axial energies E and E′ is modeled through K(E,E′,t) = (K_2^a/4)[1 − \hat{\mathbf{S}}(E,t)·\hat{\mathbf{S}}(E′,t)], where K_2^a is the two-body loss rate constant associated with the antisymmetric two-atom hyperfine state that participates in s-wave scattering. To apply this model without free parameters, K_2^a is independently measured in an incoherent 50–50 mixture by fitting the total-number decay N(t) predicted from the local relation \dot{n}(\mathbf{r},t) = − (1/4)K_2^a n^2(\mathbf{r},t).

However, when the K_2^a values extracted from 50–50 mixtures are used in the spin-lattice model for coherently prepared samples, the predictions only agree with data if those mixture-derived values are divided by two. A theoretical estimate based on the optically induced inelastic process near the 6Li Feshbach resonance yields K_2^a ≈ 69.4 μm^3/s at the applied Rabi coupling, consistent with the halved value needed for coherence experiments and inconsistent with the unhalved mixture fit. The authors note potential explanations—misapplication of the mixture decay equation in the very weakly interacting regime or an incorrect choice of the incoming two-atom state in deriving that equation—but the precise cause remains unresolved.