  We study the behaviour of the second-order correlation function in a double
cavity optomechanical system and a degenerate optical parametric amplifier
(OPA) is placed in each cavity. The first cavity is additionally driven by a
weak classical laser field. The occurrence of strong photon antibunching effect
in these two coupled cavities is observed. For suitable values of
optomechanical coupling strength as well as photon hopping process, the system
can exhibit a very strong photon antibunching effect. Our study also shows that
the unconventional photon blockade occurs in both coupling, i.e. the weak
coupling as well as in the strong coupling regimes as compared to the
conventional photon blockade which occurs only in the strong coupling regime.
We get a very strong photon antibunching effect under the unconventional photon
blockade mechanism than the conventional photon blockade mechanism. Our study
can be also used for the generation of single photon in coupled nonlinear
optomechanical systems.
