Abstract
We address propagation and entanglement of Gaussian states in optical media characterised by nontrivial spectral densities. In particular, we consider environments with a finite bandwidth J(omega ) = J_0 left[ theta (omega -Omega ) - theta (omega - Omega - delta )right] , and show that in the low temperature regime Tll Omega ^{-1}: (i) secular terms in the master equation may be neglected; (ii) attenuation (damping) is strongly suppressed; (iii) the overall diffusion process may be described as a Gaussian noise channel with variance depending only on the bandwidth. We find several regimes where propagation is not much detrimental and entanglement may be protected form decoherence.
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