Title: Scaling Enhancement of Photon Blockade in Output Fields

Abstract: Photon blockade enhancement is an exciting and promising subject that has been well studied for photons in cavities. However, whether photon blockade can be enhanced in the output fields remains largely unexplored. We show that photon blockade can be greatly enhanced in the mixing output field of a nonlinear cavity and an auxiliary (linear) cavity, where no direct coupling between the nonlinear and auxiliary cavities is needed. We uncover a biquadratic scaling relation between the second-order correlation of the photons in the output field and intracavity nonlinear interaction strength, in contrast to a quadratic scaling relation for the photons in a nonlinear cavity. We identify that this scaling enhancement of photon blockade in the output field is induced by the destructive interference between two of the paths for two photons passing through the two cavities. We then extend the theory to the experimentally feasible Jaynes-Cummings model consisting of a two-level system strongly coupled to one of the two uncoupled cavities, and also predict a biquadratic scaling law in the mixing output field. Our proposed scheme is universal and can be extended to enhance blockade in other bosonic systems.