UC Irvine

Spectroscopy, the study of matter via its interactions with light, is a vast subject that includes many of humanity's principle means of probing the fundamental structure of matter. Though usually understood from the perspective of classical light, important effects arise due to the quantum nature of the electromagnetic field. Additionally, the quantum vacuum can serve as an effective couple between molecules in the system, generating many-body interactions and cooperative processes in the material. While many techniques are well-described classically, quantum-field corrections can dominate the desired signals in certain cases, such as cascading in higher-order n-wave mixing signals, and are key for experimental interpretation. Even spontaneous emission and light scattering are best understood from the perspective of quantum fields. In this thesis, we utilize a systematic procedure, based on the density matrix in Liouville space, to give a rigorous description of elementary quantum-field effects in nonlinear spectroscopy, with specific examples made to ultrafast x-ray and optical techniques.