Quantum theory for nonlinear optical effects in the ultra-strong light-matter coupling regime

TL;DR

This paper develops a comprehensive quantum theory for nonlinear optical effects in semiconductor quantum wells under ultra-strong light-matter coupling, addressing limitations of previous models and guiding future quantum optical device design.

Contribution

It extends the PZW quantum electrodynamics framework to nonlinear regimes using a fully fermionic approach, unifying microcavity and local field effects without bosonization.

Findings

Describes impact of light-matter states on high-frequency generation.

Identifies limitations of single-particle models in ultra-strong coupling.

Proposes design principles for optimizing nonlinear conversion efficiencies.

Abstract

We present a microscopic quantum theory for nonlinear optical phenomena in semiconductor quantum well heterostructures operating in the regime of ultra-strong light matter coupling regime. This work extends the Power-Zienau-Wooley (PZW) formulation of quantum electrodynamics to account for nonlinear interactions based on a fully fermionic approach, without resorting to any bosonization approximation. It provides a unified description of the microcavity and the local field enhancement effects on the nonlinear optical response, thus encompassing the phenomena known as epsilon near zero (ENZ) effect. In particular, our theory describes the impact of the light-matter coupled states on the high frequency generation process, relevant for recent experimental investigations with polaritonic metasurfaces. We unveil the limitations of traditional single-particle approaches and propose novel design principles to optimize nonlinear conversion efficiencies in dense, microcavity-coupled electronic systems. The theoretical framework developed here provides an efficient tool for the development of advanced quantum optical applications in the mid-infrared and terahertz spectral domains. Furthermore, it establishes a foundation for exploring the quantum properties of the ultra-strong light-matter regime through frequency-converted polariton states.