Energy level structure of the coupled-cavity optomechanical system. The number states of photons and phonons are denoted by n_i (i = a,c,b,d). The tunneling coupling strength between |n_a,n_c + 1, n_b,n_d〉 and |n_a + 1, n_c,n_b,n_d〉 is J, the coupling strength between |n_a,n_c,n_b + 1,n_d〉 and |n_a + 1,n_c,n_b,n_d〉 is G_a, and the coupling strength between |n_a,n_c,n_b,n_d + 1〉 and |n_a,n_c + 1,n_b,n_d〉 is G_c.