Two-mode hyperradiant lasing in a system of two quantum dots embedded in a bimodal photonic crystal cavity

Abstract We propose a scheme for two-mode hyperradiant lasing in a system of two incoherently pumped semiconductor quantum dots (QDs) strongly coupled to a bimodal photonic crystal cavity. Exciton-phonon interactions are treated within a time-local polaron-transformed master-equation framework, allowing us to capture both resonant and off-resonant light-matter coupling regimes. We investigate collective emission through the radiance witness, mean intracavity photon numbers, and intra-and intermode second-order photon correlations. In the off-resonant regime, we show that phonon-assisted cooperative two-mode, two-photon processes significantly enhance intermode correlations and drive the system into a hyperradiant steady state, characterized by a radiance witness exceeding the superradiant limit. By deriving laser rate equations, we quantify the relative contributions of single-photon and two-photon emission and absorption channels and establish a direct connection between enhanced radiance and spectral linewidth narrowing. A comparison between single-mode and bimodal cavity configurations reveals that bimodal coupling leads to stronger cooperative emission and a substantial suppression of the emission linewidth. Our results highlight the constructive role of phonons in enabling cooperative multiphoton processes and demonstrate the potential of bimodal QD-cavity platforms for realizing steady-state hyperradiant light sources.