Hyperfine dependent atom-molecule loss analyzed by the analytic solution of few-body loss equations

We prepare mixtures of ultracold ${}^{39}\mathrm{K}$ atoms in various hyperfine spin states with ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecules in an optical dipole trap at a fixed magnetic field and study inelastic two-body atom-molecule collisions. We observe atom-molecule losses that are hyperfine dependent with a two-body loss rate far below the universal limit. We analyze the two-body loss dynamics based on the derivation of general and easy applicable analytic solutions for the differential equations describing the loss of an arbitrary number $\gamma$ of particles in a single collisional event.

Figure 1

Loss in atom-molecule mixtures. The upper part shows the two-body loss rate coefficients for the different molecular systems. The left panel includes the loss rate coefficients for the ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}+{}^{39}\mathrm{K}$ mixture with different hyperfine states for ${}^{39}\mathrm{K}$ atoms (open circles). The values for ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}+{}^{23}\mathrm{Na}$ (gray diamond, middle panel) and ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ (gray triangle, right panel) are shown for comparison. Note that the value for the $|1,-1\rangle$ state is so small that it is not shown in the graph. All measurements were performed at a temperature of 300 nK. The horizontal lines represent the respective universal limit, calculated also for 300 nK. The solid gray bar diagram in the lower part shows the number of available loss channels (left axes) due to hyperfine changing collisions for the ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}+{}^{39}\mathrm{K}$ mixture with the total $M_F=M_{i,\text{NaK}}+m_{f,\mathrm{K}}$ preserved. The dashed bar diagram indicates the number of all energetically possible decay channels (right axes), if one assumes that $M_F$ is not preserved.