Autler-Townes effect in a sodium molecular-ladder scheme

Abstract

We report results from studies of the Autler-Townes (AT) effect observed in sodium molecules from a molecular beam. A relatively weak laser field $P$ couples an initially populated rovibronic level $g$ in the electronic ground state (here $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+},{v}^{\ensuremath{''}}=0$, ${J}^{\ensuremath{''}}=7$) to a selected excited rovibronic level $e$ (here $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+},{v}^{\ensuremath{'}}=10$, ${J}^{\ensuremath{'}}=8$), which in turn is coupled by a relatively strong laser field $S$ to a more highly excited level $f$ (here $5\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+},v=10$, $J=9$), a scheme we idealize as a three-state ladder. The AT effect is seen by scanning the frequency of the $P$ field while recording fluorescence from both the $e$ and $f$ levels in separate detection channels. We present qualitative theoretical considerations showing that, when the $P$ field is weak, the ratio of doublet component areas in the excitation spectrum from level $f$ can be used to determine the lifetime of this level. We obtain a value of $17\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$. When the $P$ field is stronger, such that its Rabi frequency is larger than the decay rate of level $e$, the fraction of $f$-level population that decays to the intermediate electronic state $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ can be deduced from the AT spectrum. When supplemented with values of Franck-Condon and H\"onl-London factors, our measurements give a value for the branching ratio (the fraction returning to level $e$) of ${r}_{e}=0.145$ with a statistical error of $\ifmmode\pm\else\textpm\fi{}0.004$. The use of a strong $P$ field on the $g\text{\ensuremath{-}}e$ transition and a weak $S$ field as a probe on the $e\text{\ensuremath{-}}f$ transition results in complex line shapes in the excitation spectrum of level $f$, not showing the familiar Autler-Townes doublet structure.