Quantum theory of surface lattice resonances

TL;DR

This paper develops a quantum optical framework for surface lattice resonances in nanoparticle arrays, enabling analysis of quantum emitter interactions and nonlinear effects beyond classical models.

Contribution

It introduces a quantum input-output theory for nanoparticle lattices, extending the understanding of SLRs to include nonlinearities and quantum emitter coupling.

Findings

Derived quantum input-output relations for nanoparticle arrays.

Demonstrated coupling of SLRs with quantum emitters and vibrational modes.

Showed how emitter nonlinearities can switch SLR conditions and induce nonlinear phase-matching.

Abstract

The collective interactions of nanoparticles arranged in periodic structures give rise to high-$Q$ in-plane diffractive modes known as surface lattice resonances. While these resonances and their broader implications have been extensively studied within the framework of classical electrodynamics and linear response theory, a quantum optical theory capable of describing the dynamics of these structures, especially in the presence of material nonlinearities beyond \textit{ad hoc} few-mode approximations, is largely missing. To this end, we consider a lattice of metallic nanoparticles coupled to the electromagnetic field and derive the quantum input--output relations within the electric dipole approximation. As applications, we analyze coupling between the nanoparticle array and external quantum emitters, and show how the formalism extends to molecular optomechanics, where the high $Q$-factors of SLRs enable coupling to collective vibrational modes. We further consider arrays composed of saturable excitonic emitters, demonstrating how emitter nonlinearities can be used to switch the SLR condition between electronic transitions. Using a perturbative approach that accounts for population dynamics, we show how these effects can be probed in pump--probe experiments and give rise to nonlinear phase-matching phenomena. Our work provides a microscopic framework for modeling SLRs interacting with quantum emitters without phenomenological descriptions of the electromagnetic environment.