We study non-linear optical effects in electron systems with and without inversion symmetry in a Fabry-Perot cavity. General photon up- and down-conversion processes are modeled by the coupling of a noninteracting lattice model to two modes of the quantized light field. Effective descriptions retaining the most relevant states are devised via downfolding and a generalized Householder transformation. These models are used to relate the transition amplitudes for even order photon-conversion processes to the shift vector, a topological quantity describing the difference in polarization between the valence and conduction band in non-centrosymmetric systems. We also demonstrate that the truncated models, despite their small Hilbert space, capture correlation effects induced by the photons in the electronic subsystem.
@article{arxiv.2105.01055,
title = {Non-linear optical processes in cavity light-matter systems},
author = {Markus Lysne and Philipp Werner},
journal= {arXiv preprint arXiv:2105.01055},
year = {2021}
}