Many-photon effects in time-resolved second harmonic generation from systems in optical cavities

Abstract: Second harmonic generation is popular due to its numerous applications in different technologies dealing with multiple fields of science. The rapid technical advancement with the second harmonic generation demands parallel development in the theoretical understanding. With this view in mind, in our three papers, we theoretically investigated second harmonic generation from different systems in an optical cavity, and this thesis is based on these three papers. Our studies are with the cavity, which will confine the photon mode. Also, we can address the low photon regime with the cavity and observe the dominating quantum effects. We analyze the second harmonic generation by observing the fluorescent spectra of the system with time-resolved formalism. In our studies, we also propose a quantum-classical method inspired bythe physics of the Caldeira-Leggett model to depict cavity leakage.In Paper I, we study fluorescent spectra from a Hubbard dimer. As a novelty in the study, along with electron and photon degrees of freedom, we also consider quantum description for nuclear degrees of freedom. With this new description of the Hubbard dimer, we demonstrated a competition between photo-induced dimer dissociation and second harmonic generation.In Paper II, we investigate the fluorescent spectra of cold boson atoms in an optical lattice and also from a Bose-Einstein condensate. The study outlines the effects of increasing the number of atoms, lattice sites, and the atom-atom interaction on second harmonic generation.In Paper III, we explore the non-equilibrium Green function method as an alternative to investigate second harmonic generation from a larger Dicke system. In the study, we observe the effect of disorder and electron interaction on second harmonic generation.