Non-linear optical processes in cavity light-matter systems
arXiv:2105.01055 · doi:10.1103/PhysRevB.104.035209
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.
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