Unified Effective Field Theory for Nonlinear and Quantum Optics

TL;DR

This paper introduces a unified effective field theory that bridges quantum and nonlinear optics, accurately predicting phenomena across regimes by coupling electromagnetic fields with material polarization and including dissipative effects.

Contribution

It develops a comprehensive theoretical framework that unifies quantum and nonlinear optical phenomena, incorporating gauge symmetry, dissipation, and material-specific susceptibilities.

Findings

Reproduces measured third-order susceptibilities across frequencies.

Accurately models real-time dynamics of polariton systems.

Validates predictions with experimental data for various materials.

Abstract

Predicting phenomena that mix few-photon quantum optics with strong field nonlinear optics is hindered by the use of separate theoretical formalisms for each regime. We close this gap with a unified effective field theory valid for frequencies lower than the material-dependent cutoff set by the band gap, plasma frequency, or similar scale. The action couples the electromagnetic gauge field to vector polarisation modes. An isotropic potential generates the optical susceptibilities, while a higher-dimension axion-like term captures magnetoelectric effects; quantisation on the Schwinger-Keldysh contour with doubled BRST ghosts preserves gauge symmetry in dissipative media. One-loop renormalisation-group equations reproduce the measured dispersion of the third-order susceptibility from terahertz to near-visible frequencies after matching a single datum per material. Real-time dynamics solved with a matrix-product-operator engine yield good agreement with published results for GaAs polariton cavities, epsilon-near-zero indium-tin-oxide films and superconducting quarton circuits. The current formulation is limited to these 1-D geometries and sub-cut-off frequencies; higher-dimensional or above-cut-off phenomena will require additional degrees of freedom or numerical methods.