Cascaded Optomechanical systems

We study the dynamics of a pair of optomechanical systems interacting dissipatively with a wave guide in a unidirectional way. We investigate the behaviour of both classical and quantum correlations established between the two mechanical modes both in the transient and in the stationary regime. We find that a constant amount of steady correlations can exists at long times. We furthermore analyze the power spectrum of the output guide field and we show how from such spectrum it is possible to reconstruct the spectra of each single mirror. Finally we show that that, thanks to the unidirectional coupling, a temperature gradient between the mirrors depending on the frequencies detuning is established .