  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.
