Measurement of NaK $3^1\Pi \to X^1\Sigma ^+,A^1\Sigma ^+$ Absolute Transition Dipole Moment Functions using Autler-Townes Spectroscopy and Calibrated Fluorescence

We describe a two-laser experiment using OODR and Autler-Townes splittings to determine NaK $3^1\Pi \to X^1\Sigma ^+,A^1\Sigma ^+$ absolute transition dipole moment functions. Resolved $3^1\Pi \to A^1\Sigma ^+$ and $3^1\Pi \to X^1\Sigma ^+$ fluorescence is recorded with the frequencies of a Ti:Sapphire laser (L1) and a ring dye laser (L2) fixed to excite particular $3^1\Pi \left( {19,11,f} \right)\leftarrow 2\left( A \right)^1\Sigma ^+\left( {{v}',11,e} \right)\leftarrow 1\left( X \right)^1\Sigma ^+\left( {{v}'',J\pm 1,e} \right)$ transitions. The coefficients of a trial transition dipole moment function $\mu \left( R \right)=a_0 +a_1 R^{-2}+a_2 R^{-4}+...$ are adjusted to match the relative intensities of resolved spectral lines terminating on $A^1\Sigma ^+\left( {{v}',11,e} \right)$ and $X^1\Sigma ^+\left( {{v}'',11,e} \right)$ levels. These data provide a \textit{relative} measure of the function $\mu \left( R \right)$ over a broad range of $R$. Next L2 is tuned to the specific $3^1\Pi \left( {19,11,f} \right)\leftarrow A^1\Sigma ^+\left( {10,11,e} \right)$ transition and focused to an intensity large enough to split the levels via the Autler-Townes effect. L1 is scanned over the $A^1\Sigma ^+\left( {10,11,e} \right)\leftarrow X^1\Sigma ^+\left( {1,J\pm 1,e} \right)$ transition to probe the AT lineshape, which is fit using density matrix equations to yield an \textit{absolute} value for $\left| {\left\langle {3^1\Pi \left( {19,11,f} \right)\left| {\mu \left( R \right)} \right|A^1\Sigma ^+\left( {10,11,e} \right)} \right\rangle } \right|$. This value is used to place the relative $\mu \left( R \right)$ obtained with resolved fluorescence onto an absolute scale. We compare with recent theoretical results.