Cumulant expansion for the treatment of light-matter interactions in arbitrary material structures

TL;DR

This paper introduces a cumulant expansion method to model light-matter interactions in complex nanophotonic environments, capturing quantum effects with reduced computational effort compared to full quantum treatments.

Contribution

It develops and benchmarks a cumulant expansion approach for quantum emitter interactions with arbitrary photonic spectral densities, enabling efficient simulations in complex environments.

Findings

Accurately models dynamics in complex photonic environments

Benchmarking shows good agreement with exact solutions

Method reduces computational complexity for quantum light-matter systems

Abstract

Strong coupling of quantum emitters with confined electromagnetic modes of nanophotonic structures may be used to change optical, chemical and transport properties of materials, with significant theoretical effort invested towards a better understanding of this phenomenon. However, a full theoretical description of both matter and light is an extremely challenging task. Typical theoretical approaches simplify the description of the photonic environment by describing it as a single or few modes. While this approximation is accurate in some cases, it breaks down strongly in complex environments, such as within plasmonic nanocavities, and the electromagnetic environment must be fully taken into account. This requires the quantum description of a continuum of bosonic modes, a problem that is computationally hard. We here investigate a compromise where the quantum character of light is taken into account at modest computational cost. To do so, we focus on a quantum emitter that interacts with an arbitrary photonic spectral density and employ the cumulant or cluster expansion method to the Heisenberg equations of motion up to first, second and third order. We benchmark the method by comparing with exact solutions for specific situations and show that it can accurately represent dynamics for many parameter ranges.