  In this work we investigate an optomechanical system consisting of two
cavities coupled to the same mechanical resonator. We consider each cavity
being weakly pumped as well as a small tunneling rate between the cavities. In
such conditions, the system can be studied via quantum Langevin equations and
the steady state solution can be found perturbatively. In order to ensure that
the approximations and methods used to study the system are suitable, the
analytical results were compared to numerical simulations. We study the
statistical properties of the cavity radiation fields and we show that
depending on the values of the parameters of the system, it is possible to
modify the spectrum of the cavities and even enhance the sub-Poissonian
character of the cavity field.
