Cooperative Suppression of Two-Particle Excitation by Kerr Nonlinearity and Cavity Loss ion a Driven Holstein-Tavis-Cumming System

We apply the numerically accurate multiple Davydov Ansatz (multi-$\rm D_2$) method to investigate the nonequilibrium dynamics of an open molecular cavity system using an extended driven-dissipative Holstein-Tavis-Cummings model incorporating Kerr nonlinearity. Our results reveal that the synergy between Kerr nonlinearity and exciton-phonon coupling induces an anharmonic level structure, imposing a stringent energy penalty that isolates the one-excitation manifold. This establishes a robust single-excitation-dominated regime that dynamically manifests photon blockade, characterized by suppression of the pure two-photon state and isolation of the one-excitation manifold. While strong coherent driving induces power broadening that overcomes the nonlinear barrier and opens multiphoton channels, cavity dissipation counteracts this process by acting as a highly selective manifold filter. By preferentially depleting fragile multi-photon states while sheltering single excitations within dissipation-free dark states, the cavity mode decay rate actively cooperates with Kerr nonlinearity to restore and reinforce the photon blockade effect. These findings elucidate the intricate interplay among nonlinearity, driving, and dissipation, offering a theoretical blueprint for engineering robust single-photon sources in open molecular cavity platforms.