Conical Intersections (CIs) in a molecule originate from the breakdown of the Born-Oppenheimer approximation when electronic states come close in energy. Ultrafast non-radiative decay channels open up in the vicinity of a CI, thus funneling a molecule from one electronic state to another. Observing such non-adiabatic processes can be challenging since they take place at the timescale of femtoseconds. Therefore, we use non-linear spectroscopy to probe the existence of CIs and the non-adiabatic processes in their vicinity. In this thesis, we discuss non-linear spectroscopic methods that may probe CIs in a molecule. The CI in the pyrrole molecule is probed using transient X-ray absorption, time-resolved X-ray spontaneous emission, and off-resonant Ra-man spectroscopies. Time-resolved photoelectron spectroscopy is found useful in observing the separation between the electronic states and the electronic coherence near a CI simultaneously.

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.