Limits of Perturbation Theory for Multimode Light Propagation in Dispersive Optical Cavities

TL;DR

This paper investigates the limitations of perturbation theory in modeling multimode quantum light propagation in dispersive optical cavities, highlighting the conditions under which the approach remains valid or breaks down.

Contribution

It introduces a perturbation-theory-based method to analyze group velocity dispersion effects in optical cavities and assesses its validity against rigorous solutions.

Findings

Perturbation theory is valid within specific parameter regimes.

Key parameters like mode order and dispersion strength influence the theory's accuracy.

The study delineates the limits of perturbative approaches in multimode quantum systems.

Abstract

Temporal modes of quantum light pulses is a promising resource for modern quantum technologies, driving advancements in quantum computing, communication, and metrology. Precise control and manipulation of these modes remain critical challenges, particularly in systems where nonlinear multimode dynamics interact with dispersion effects. In this work, we focus on the role of group velocity dispersion (GVD) within optical cavities - a phenomenon traditionally viewed as detrimental but increasingly recognized as a versatile tool for quantum light manipulation. We present a perturbation-theory-based approach to analyze GVD effects in a synchronously pumped dispersive cavity. By comparing perturbative solutions to rigorous steady-state results, we establish the validity region of the perturbative approach and assess its limitations in multimode systems. Our study identifies key parameters governing the breakdown of perturbation theory, such as mode order, dispersion strength, and cavity decay rates.