Green's function approach to interacting lattice polaritons and optical nonlinearities in subwavelength arrays of quantum emitters

TL;DR

This paper introduces a Green's function method to analytically study nonlinear optical interactions in subwavelength arrays of quantum emitters, advancing understanding of photon-photon interactions and many-body effects.

Contribution

The paper presents a diagrammatic Green's function approach for analytical investigation of nonlinear processes in 2D quantum emitter arrays, complementing numerical methods.

Findings

Derived a simple scattering matrix expression for photon interactions.

Reproduced numerical simulation results analytically.

Provided insights into nonlinear optical responses.

Abstract

Sub-wavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed photon-losses and emerging optical nonlinearities due to strong photon-coupling to mesoscopic numbers of emitters holds promise for generating nonclassical light and engineering effective interactions between freely propagating photons. While most studies have thus far relied on numerical simulations, we describe here a diagrammatic Green's function approach that permits analytical investigations of nonlinear processes. We illustrate the method by deriving a simple expression for the scattering matrix that describes photon-photon interactions in an extended two-dimensional array of quantum emitters, and reproduces the results of numerical simulations of coherently driven arrays. The approach yields intuitive insights into the nonlinear response of the system and offers a promising framework for a systematic development of a theory for interacting photons and many-body effects on collective radiance in two-dimensional arrays of quantum emitters.