Photonic rogue waves in a strongly dispersive coupled-cavity array involving self-attractive Kerr nonlinearity

Based on the combined Dicke, Bose-Hubbard, and Lipkin-Meshkov-Glick Hamiltonian, we investigate the formation of photonic rogue waves, including their Akhmediev and Kuznetsov-Ma cousins, in the strongly dispersive regime of a generalized atom-cavity array configuration. By means of the multiple-scale approach and mean-field approximation, we unveil that, due to the interplay between the photon hopping-induced tunneling effect and the self-attractive nonlinearity, the photons can redistribute in the whole array, which in turn leads to the redistribution (creation or annihilation) of excited atoms in each cavity and, consequently, the occurrence of Peregrine soliton states in both photonic and atomic fields. This interplay also yields an interesting intensity-clamping effect that the sum of the peak intensities of both rogue waves will be constant, although this quantity varies from site to site. We numerically confirm the analytical predictions, showing that the Peregrine rogue waves generated are stable against perturbations, despite the onset of modulation instability.