  In this paper, we investigate the generation of continuous variable
entanglement between two spatially-separate nanocavities mediated by a coupled
resonator optical waveguide in photonic crystals. By solving the exact dynamics
of the cavity system coupled to the waveguide, the entanglement and purity of
the two-mode cavity state are discussed in detail for the initially separated
squeezing inputs. It is found that the stable and pure entangled state of the
two distant nanocavities can be achieved with the requirement of only a weak
cavity-waveguide coupling when the cavities are resonant with the band center
of the waveguide. The strong couplings between the cavities and the waveguide
lead to the entanglement sudden death and sudden birth. When the frequencies of
the cavities lie outside the band of the waveguide, the waveguide-induced cross
frequency shift between the cavities can optimize the achievable entanglement.
It is also shown that the entanglement can be easily manipulated through the
changes of the cavity frequencies within the waveguide band.
