  We investigate the controllable generation of robust photon entanglement with
a circuit cavity electromechanical system, consisting of two superconducting
coplanar waveguide cavities (CPWC's) capacitively coupled by a nanoscale
mechanical resonator (MR). We show that, with this electromechanical system,
two-mode continuous-variable entanglement of cavity photons can be engineered
deterministically either via coherent control on the dynamics of the system, or
through a dissipative quantum dynamical process. The first scheme, operating in
the strong coupling regime, explores the excitation of the cavity Bogoliubov
modes, and is insensitive to the initial thermal noise. The second one is based
on the reservoir-engineering approach, which exploits the mechanical
dissipation as a useful resource to perform ground state cooling of two
delocalized cavity Bogoliubov modes. The achieved amount of entanglement in
both schemes is determined by the relative ratio of the effective
electromechanical coupling strengths, which thus can be tuned and made much
lager than that in previous studies.
