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We investigate theoretically the temporal evolution of a squeezed state inlossy coupled-cavity systems. We present a general formalism based upon thetight binding approximation and apply this to a two-cavity system as well as toa coupled resonator optical waveguide in a photonic crystal. We deriveanalytical expressions for the number of photons and the quadrature noise ineach cavity as a function of time when the initial excited state is a squeezedstate in one of the cavities. We also analytically evaluate the time dependantcross correlation between the photons in different cavities to evaluate thedegree of quantum entanglement. We demonstrate the effects of loss on theproperties of the coupled-cavity systems and derive approximate analyticexpressions for the maximum photon number, maximum squeezing and maximumentanglement for cavities far from the initially excited cavity in a losslesscoupled resonator optical waveguide.

Squeezed state evolution and entanglement in lossy coupled resonator optical waveguides