Collective and nonlinear dynamics in spatially structured and spectrally inhomogeneous emitter ensembles

Ordered emitters coupled to photonic baths realise uniquely cooperative light-matter platforms with applications to analogue quantum simulation and photonic state generation. On the other hand, spectral inhomogeneity in spatially homogeneous systems can enable novel technologies such as atomic frequency combs and quantum memories. However, the difficulty of theoretically studying large spatially and spectrally inhomogeneous spin systems has hindered our understanding and ability to exploit them in tandem. Here we advance the theory of and shed light on the optical response and dynamics of spatially ordered systems of solid-state emitters featuring spectral inhomogeneity. We first show at the single-photon level how such lattices can exhibit huge optical response and broad cooperative resonances that exceed the inhomogeneous line in experimentally relevant scenarios. We then move to investigate nonlinear dynamics under initial population inversion and determine generic conditions on spectral homogeneity that permit superradiant bursts via formation of macroscopic coherence overcoming spectral broadening. Our results reconcile spectral inhomogeneity with the rich world of ordered emitter arrays and open the path for exploring their combined potential applications.