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We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight binding approximation and apply this to a two-cavity system as well as to a coupled resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time dependant cross correlation between the photons in different cavities to evaluate the degree of quantum entanglement. We demonstrate the effects of loss on the properties of the coupled-cavity systems and derive approximate analytic expressions for the maximum photon number, maximum squeezing and maximum entanglement for cavities far from the initially excited cavity in a lossless coupled resonator optical waveguide.

We present an integrated source of counterpropagating entangled states based on a coupled resonator optical waveguide that is pumped by a classical pulsed source incident from above the waveguide. We investigate theoretically the generation and propagation of continuous variable entangled states in this coupled-cavity system in the presence of intrinsic loss. Using a tight-binding approximation, we derive analytic time-dependent expressions for the number of photons in each cavity, as well as for the correlation variance between the photons in different pairs of cavities, to evaluate the degree of quantum entanglement. We also derive simple approximate expressions for these quantities that can be used to guide the design of such systems, and discuss how pumping configurations and physical properties of the system affect the photon statistics and the degree of quantum correlation. * hossein.seifoory@queensu.ca

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