Measurement of dynamic Stark polarizabilities by analyzing spectral line shapes of forbidden transitions

Abstract

We present a measurement of the dynamic scalar and tensor polarizabilities of the excited state $|5d6s {}^{3}{D}_{1}\ensuremath{\rangle}$ in atomic ytterbium. The polarizabilities were measured by analyzing the spectral lineshape of the 408-nm $6{s}^{2} {}^{1}{S}_{0}\ensuremath{\rightarrow}5d6s {}^{3}{D}_{1}$ transition driven by a standing wave of resonant light in the presence of static electric and magnetic fields. Due to the interaction of atoms with the standing wave, the lineshape has a characteristic polarizability-dependent distortion. A theoretical model was used to simulate the lineshape and determine a combination of the polarizabilities of the ground and excited states by fitting the model to experimental data. This combination was measured with a 13$%$ uncertainty, only 3$%$ of which was due to uncertainty in the simulation and fitting procedure. By comparing two different combinations of polarizabilities, the scalar and tensor polarizabilities of the state $|5d6s {}^{3}{D}_{1}\ensuremath{\rangle}$ were measured to be ${\ensuremath{\alpha}}_{0}({}^{3}{D}_{1})=0.009(21) {\mathrm{Hz}(\mathrm{V}/\mathrm{cm})}^{\ensuremath{-}2}$ and ${\ensuremath{\alpha}}_{2}({}^{3}{D}_{1})=\ensuremath{-}0.103(26) \mathrm{Hz}(\mathrm{V}/\mathrm{cm}){}^{\ensuremath{-}2}$, respectively. We show that this technique can be applied to similar atomic systems.