Using system-reservoir methods to derive effective field theories for broadband nonlinear quantum optics: a case study on cascaded quadratic nonlinearities

TL;DR

This paper introduces a perturbative system-reservoir framework to derive effective field theories for broadband nonlinear quantum optics, exemplified by cascaded quadratic nonlinearities, enabling simplified yet accurate modeling of complex quantum optical dynamics.

Contribution

It develops a novel perturbative approach combining diagonalization and master equations to derive effective models for broadband nonlinear quantum optical systems, specifically for cascaded quadratic nonlinearities.

Findings

Effective models capture self- and cross-phase modulation dynamics.

Emergence of two-photon loss channels in reduced models.

Conditions for model accuracy in dispersive and dissipative regimes.

Abstract

In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical $\chi^{(2)}$ (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics.