Hidden order in quantum many-body dynamics of driven-dissipative nonlinear photonic lattices

We study the dynamics of nonlinear photonic lattices driven by two-photon parametric processes. By means of matrix-product-state-based calculations, we show that a quantum many-body state with long-range hidden order can be generated from the vacuum. Although this order resembles that characterizing the Haldane insulator, our system is far from equilibrium due to the drive and photon loss. A possible explanation highlighting the role of the symmetry of the drive and the effect of photon loss is discussed. An implementation based on superconducting circuits is proposed and analyzed.