How Subradiance Enables Nonlinearity in Weakly Driven Quantum Arrays

Harnessing the nonlinear response of a medium is essential for applications including frequency conversion and light amplification, as well as for the generation of quantum many-body correlations of light or matter. However, achieving these effects typically requires high drive intensities and thick samples, which induce undesired heating effects that typically suppress quantum correlations. In this work, we demonstrate that atom-thin arrays of quantum emitters exhibit a robust nonlinear response even at arbitrarily weak drive intensities. This discovery challenges the long-held assumption that weakly driven ensembles behave classically; instead, we reveal that subradiant states provide a dominant nonlinear contribution that persists in the low-intensity limit. Using a Dynamical Mean-Field Theory (DMFT) approach, we predict that these nonlinearities generate a quantum-correlated steady state composed of interacting pairs of subradiant excitations, characterized by long-range correlations and multi-mode squeezing. Our findings establish a new frontier for nonlinear quantum optics at minimal power, and provide a scalable protocol for preparing multimode squeezing, offering potential for applications in quantum metrology.

💡 Research Summary

The paper investigates the nonlinear optical response of atom‑thin arrays of two‑level quantum emitters when driven by an arbitrarily weak coherent field. Conventional wisdom holds that weakly driven ensembles behave linearly and can be described by classical equations of motion, because subradiant collective modes—those with suppressed radiative decay—are dark to far‑field illumination and therefore remain unpopulated. The authors overturn this view by showing that, in large periodic arrays with sub‑wavelength spacing (k₀a≈2), pairs of drive photons can resonantly scatter into pairs of subradiant excitations via a parametric‑type process.

Starting from a Markovian master equation that includes long‑range dipole‑dipole interactions V₍ij₎ and collective decay rates Γ₍ij₎, the authors Fourier‑transform to momentum space, obtaining dispersion Vₖ and decay Γₖ. For |k|>k₀ the decay vanishes, defining the subradiant band. A naïve bosonic (non‑interacting) approximation would predict no population of these modes under weak drive (Ω≪Γₖ). However, a second‑order perturbative treatment reveals an effective Hamiltonian of the form
H_eff≈∑ₖ