Non-linear optical processes in cavity light-matter systems

TL;DR

This paper investigates non-linear optical effects in cavity electron systems, linking photon conversion processes to topological polarization differences and demonstrating that simplified models can capture photon-induced electronic correlations.

Contribution

It introduces effective models for non-linear optics in cavity systems that connect photon conversion to topological polarization and show correlation effects with minimal Hilbert space.

Findings

Photon up- and down-conversion processes relate to the shift vector.

Truncated models capture photon-induced electronic correlations.

Effective models simplify analysis of non-linear optical effects.

Abstract

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.