Theory of laser-induced associative ionization of ultracold Na

Abstract

The rate coefficient for the laser-induced associative-ionization reaction of ultracold Na in an optical trap is calculated as a function of the trap laser detuning from the Na${(}^{2}$${\mathit{S}}_{1/2}$,F=2)\ensuremath{\rightarrow}Na${(}^{2}$${\mathit{P}}_{3/2}$,F=3) resonance. Aided by a knowledge of the excited-state potential-energy curves and of the nature of the free-atom optical-pumping process, we propose the following mechanism, which we call photoassociative ionization (PAI): 2Na${(}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}^{+}$)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$${\mathrm{Na}}_{2}^{\mathrm{*}}$(${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ and ${1}_{\mathit{g}}$)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$${\mathrm{Na}}_{2}^{\mathrm{*}\mathrm{*}}$(${1}_{\mathit{u}}$)\ensuremath{\rightarrow}${\mathrm{Na}}_{2}^{+}$+${\mathit{e}}^{\mathrm{\ensuremath{-}}}$. Maxima in the calculated PAI rate coefficient occur at detunings that are simultaneously one-photon resonant with bound levels of the long-range ${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ state and two-photon resonant with the lower rotational levels of a vibrational level lying 9 GHz below the dissociation threshold of the autoionizing ${1}_{\mathit{u}}$ state. The calculated PAI spectrum (PAI rate coefficient versus trap-laser detuning) displays a series of broad peaks between -0.5 and -4 GHz detuning and a cutoff at -5 GHz detuning, as does the experimentally measured spectrum of Lett et al. [Phys. Rev. Lett. 67, 2139 (1991)].The broad widths of the peaks in the PAI spectrum is due in part to the orientation averaging of the collision vector with respect to the electric-field vector and to the optical pumping of the ${\mathrm{Na}}_{2}$\ensuremath{\rightarrow}${\mathrm{Na}}_{2}^{\mathrm{*}}$ rovibronic transition. The calculated PAI rate coefficient at -0.6 GHz detuning is a factor of 4 higher than the experimental value. Fine-structure-changing transitions play a role in the doubly excited states, because of the ${1}_{\mathit{u}}$ avoided crossing, but not in the intermediate states, because they have gerade symmetry and the only states that have been shown to undergo fine-structure-changing transitions with large probability have ungerade symmetry. Several predictions based on the proposed model and suggestions for future experiments are discussed.