Enhancement of the formation of ultracold ${}^{85}$Rb${}_2$ molecules due to resonant coupling

We have studied the effect of resonant electronic state coupling on the formation of ultracold ground-state ${}^{85}$Rb${}_2$. Ultracold Rb${}_2$ molecules are formed by photoassociation (PA) to a coupled pair of $0_u^{+}$ states, $0_u^{+}(P_{1\mathrm{/}2})$ and $0_u^{+}(P_{3\mathrm{/}2})$, in the region below the $5S+5P_{1\mathrm{/}2}$ limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X^1{\mathrm{\Sigma }}_g^{+}$. The population distribution of these $X$ state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2^1{\mathrm{\Sigma }}_u^{+}$ state. We find that the populations of vibrational levels $v^{\mathrm{\prime }\mathrm{\prime }}$=112$-$116 are far larger than can be accounted for by the Franck-Condon factors for $0_u^{+}(P_{1\mathrm{/}2})\to X^1{\mathrm{\Sigma }}_g^{+}$ transitions with the $0_u^{+}(P_{1\mathrm{/}2})$ state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of $0_u^{+}$ state vibrational levels. Both of these effects are explained by a new calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two $0_u^{+}$ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.