Theory of Molecular Axis Distribution Anisotropy in Ultrafast Transient Absorption Spectroscopy*

We investigate the role of molecular axis alignment distribution relative to the polarization of the interacting laser pulse in gas-phase Transient Absorption experiments. The molecular axis is linked to the electronic coherence of the excited states, shaping the dynamics of ultrafast light-matter interactions. We calculate the Lab Frame first-order and third-order polarization spectra in terms of Molecular Frame quantities. By comparing our results with the Time-Dependent Schrödinger Equation calculations, we demonstrate that the conventional approach of averaging over all molecular orientations captures only the isotropic contribution of the molecular axis distribution. However, our formalism can also account for the anisotropic contributions in the experimental spectra. This formalism is a significant step towards reconstructing Lab Frame density matrices of molecules to achieve Ultrafast Quantum Tomography through Transient Absorption Spectroscopy.