Nonlinearities and High-Harmonic Generation with Strongly Coupled Photon-Matter

<br/>The ability to generate and control light at increasingly short time scales impacts wide-ranging areas of science and technology ranging from the investigation of material properties to the development of optical frequency combs suitable for metrology. Ultrafast light sources are often limited in terms of achievable photon energies though various techniques aimed at generating high harmonics of input light from solid-state materials have been pursued to push the upper energy limit to the extreme ultraviolet or x-ray regime. In this context, I will discuss a cavity-mediated approach to break the inversion symmetry allowing for highly tunable even-order harmonic generation naturally forbidden in such systems. This relies on a quantized treatment of the coupled light-matter system, similar to the driven case, where the molecular matter is confined within an electromagnetic environment and the incident (pump) field is treated as a quantized field in a coherent state. When the light-molecule system is strongly coupled, it leads to two important features: (i) a controllable strong-coupling-induced symmetry breaking, and (ii) a tunable and highly efficient nonlinear conversion efficiency of the harmonic generation processes. Both of these have implications for molecular quantum architectures. At the same time, being able to control molecules at a quantum level gives us access to degrees of freedom such as the vibrational or rotational degrees to the internal state structure. Towards this, we explore the role an excited cavity mode plays in the generation of entanglement between molecules in a strongly coupled cavity setup and the potential for generating non-classical states of light due to the strong interaction between the molecules and cavity field. Finally, I will present an outlook on connecting ideas in cavity control of matter and nonlinearities in such systems with quantum information science.