Measurement of the electronic transition dipole moment by Autler-Townes splitting: Comparison of three- and four-level excitation schemes for the Na ₂ A ¹∑ _u ⁺ -X ¹∑ _g ⁺ system

We present a fundamentally new approach for measuring the transition dipole moment of molecular transitions, which combines the benefits of quantum interference effects, such as the Autler-Townes splitting, with the familiar R -centroid approximation. This method is superior to other experimental methods for determining the absolute value of the R -dependent electronic transition dipole moment function μe (R), since it requires only an accurate measurement of the coupling laser electric field amplitude and the determination of the Rabi frequency from an Autler-Townes split fluorescence spectral line. We illustrate this method by measuring the transition dipole moment matrix element for the Na2 A Σu+1 (v′ =25, J′ =20e) -X Σg+1 (v″ =38, J″ =21e) rovibronic transition and compare our experimental results with our ab initio calculations. We have compared the three-level (cascade) and four-level (extended Λ) excitation schemes and found that the latter is preferable in this case for two reasons. First, this excitation scheme takes advantage of the fact that the coupling field lower level is outside the thermal population range. As a result vibrational levels with larger wave function amplitudes at the outer turning point of vibration lead to larger transition dipole moment matrix elements and Rabi frequencies than those accessible from the equilibrium internuclear distance of the thermal population distribution. Second, the coupling laser can be "tuned" to different rovibronic transitions in order to determine the internuclear distance dependence of the electronic transition dipole moment function in the region of the R -centroid of each coupling laser transition. Thus the internuclear distance dependence of the transition moment function μe (R) can be determined at several very different values of the R centroid. The measured transition dipole moment matrix element for the Na2 A Σu+1 (v′ =25, J′ =20e) -X Σg+1 (v″ =38, J″ =21e) transition is 5.5±0.2 D compared to our ab initio value of 5.9 D. By using the R -centroid approximation for this transition the corresponding experimental electronic transition dipole moment is 9.72 D at Rc =4.81 Å, in good agreement with our ab initio value of 10.55 D.