Statistical product distributions for ultracold reactions in external fields

The main limitation of most ultracold chemistry studies to date is the lack of an analysis of reaction products. Here, we discuss a generally tractable, rigorous theoretical framework for computing statistical product-state distributions for ultracold reactions in external fields. We show that fields have two main effects on the products of a statistical reaction, by (1) modifying the product energy levels and thus potentially reshaping the product distributions and/or (2) adding or removing product states by changing the reaction exothermicity. By analyzing these effects and the strength of the formalism to distinguish between different reaction mechanisms in benchmark reactions involving ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ species, we argue that statistical predictions will help understanding product formation and control, and lead developments to realize the full potential of ultracold chemistry.

Figure 1

Experimental and statistical rates for ultracold reactions between ground-state ${}^{40}{\mathrm{K}}^{87}\mathrm{Rb}$ molecules in (a) magnetic, $F_{\mathrm{m}}$, and (b) electric, $F_{\mathrm{e}}$, fields $\left(d_{\mathrm{eff}}^{\mathrm{KRb}}\propto F_{\mathrm{e}}\right)$.

Figure 2

Statistical translational energy distributions for the ultracold reaction between ground-state ${}^{40}\mathrm{K}$ and ${}^{87}{\mathrm{Rb}}_2$ (red, solid) at (a) low and (b) high electric fields. The distributions for a free rotor (green, dashed) and pendular states (blue, dotted) are shown for comparison.

Figure 3

Statistical product translational energy distributions for the ultracold reaction ${}^{40}{\mathrm{K}}^{87}\mathrm{Rb}+{}^{40}{\mathrm{K}}^{87}\mathrm{Rb} \to {\mathrm{K}}_2+{\mathrm{Rb}}_2$, at different electric fields.

Figure 4

Statistical rotational distributions for the products ${}^{40}{\mathrm{K}}_2$ (red) and ${}^{87}{\mathrm{Rb}}_2$ (green) of the ultracold reaction between two ground-state ${}^{40}{\mathrm{K}}^{87}\mathrm{Rb}$ molecules in an electric field. Solid or dashed lines correspond to the case where nuclear spins are conserved or relaxed in the reaction.