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)→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${(}^3$ ${\mathrm{\Sigma }}_{\mathit{u}}^{+}$)${\to }^{\mathrm{ħ}\mathrm{\omega }}$ ${\mathrm{Na}}_2^{\mathrm{*}}$($0_{\mathit{g}}^{\mathrm{-}}$ and $1_{\mathit{g}}$)${\to }^{\mathrm{ħ}\mathrm{\omega }}$ ${\mathrm{Na}}_2^{\mathrm{*}\mathrm{*}}$($1_{\mathit{u}}$)→${\mathrm{Na}}_2^{+}$+${\mathit{e}}^{\mathrm{-}}$. Maxima in the calculated PAI rate coefficient occur at detunings that are simultaneously one-photon resonant with bound levels of the long-range $0_{\mathit{g}}^{\mathrm{-}}$ 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)].