Nanophotonic control of collective many-body states in Kerr solitons

Spatially periodic systems of coupled bosons are governed by on-site interactions and tunneling between sites, opening a rich phase space of many-body behavior. Here, we explore nanophotonic control of collective many-body light states in a driven-dissipative Kerr microresonator. We demonstrate a non-equilibrium Mott insulator to superfluid transition that arises from the interplay of spatially local Kerr interactions that generate and mediate interference among discrete frequency modes. A photonic-crystal (PhC) lattice bandgap inscribed on the resonator controls linear mode coupling while preserving self-mode Kerr interactions. By increasing the PhC bandgap, we suppress nonlinear cross-mode coupling to access the Mott-insulator phase, wherein the soliton spectrum forms a flattop frequency comb with large and uniform power per mode. In contrast, reducing the PhC bandgap restores cross-mode coupling and drives a delocalized superfluid regime characterized by long-range phase coherence and a spectrum with non-uniform power distribution. Our work shows that many-body physics creates collective states in driven-dissipative systems, enabling advances in programmable photonics and quantum-optical computing.