Non-linear Spectroscopy of Conical Intersections with XUV and X-ray Photons

Conical intersections (CIs) appear in a molecule due to the breakdown of the Born-Oppenheimer approximation when the energy difference between two or more electronic states decreases. CIs are known to play a crucial role in processes such as photosynthesis and vision in the human eye, and therefore it is important to probe the existence of such entities in molecules. Observing phenomena such as population transfer, electronic coherence generation, and vanishing electronic states separation can help probe a CI in a molecule. However, the accurate observation of the occurrence of CIs is challenging primarily due to the femtosecond time scale of such non-adiabatic processes in molecules. This thesis explores non-linear spectroscopic methods that can help detect the presence of a CI in a molecule. Multiple techniques such as photoelectron spectroscopy, transient absorption, spontaneous emission, and Raman spectroscopy with classical and entangled photons were theoretically investigated. Special emphasis was placed on observing electronic coherence near a CI, as it provides compelling evidence for the presence of a CI in a molecule. The significance of attosecond pulse trains was investigated in time-resolved photoelectron spectroscopy to improve the visibility of electronic coherence and population transfer features. A two-dimensional extension of the Raman technique TRUECARS was developed to generate Raman signals that lack vibrational coherence, thus helping visualize electronic coherences in a molecule. Entangled photons were also employed in Raman spectroscopy to probe CIs with simultaneously high temporal and spectral resolutions, which is unachievable by classical pulses.