  We propose an experimentally accessible superconducting quantum circuit,
consisting of two coplanar waveguide resonators (CWRs), to enhance the
microwave squeezing via parametric down-conversion (PDC). In our scheme, the
two CWRs are nonlinearly coupled through a superconducting quantum interference
device embedded in one of the CWRs. This is equivalent to replacing the
transmission line in a flux-driven Josephson parametric amplifier (JPA) by a
CWR, which makes it possible to drive the JPA by a quantized microwave field.
Owing to this design, the PDC coefficient can be considerably increased to be
about tens of megahertz, satisfying the strong-coupling condition. Using the
Heisenberg-Langevin approach, we numerically show the enhancement of the
microwave squeezing in our scheme. In contrast to the JPA, our proposed system
becomes stable around the critical point and can generate stronger transient
squeezing. In addition, the strong-coupling PDC can be used to engineer the
photon blockade.
