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Recently, experiments in the group of Takao Aoki at Waseda University in Japan have demonstrated coherent coupling of two nanofibre cavity-quantum electrodynamic (QED) systems separated by a distance of more than a meter . Transmission spectra show dressed states of the atoms in the two cavities with a normal mode of the cavity/coupling fibre/cavity system that is dark in the coupling fibre, hence offering a robust, coherent channel between the two distant atom-cavity systems. Complementary to this, another experiment  has demonstrated the existence of a dressed state of the distant atoms with only the coupling fibre, i.e., a dressed state that is dark in the two cavity modes. These phenomena are qualitatively well described by a relatively simple quantum optical model based upon treating the cavity and coupling fibre fields as single modes, with losses accounted for in a master equation approach. However, the long lengths of the cavities and the relatively low reflectivities of the (fibre Bragg grating) mirrors mean that the single-mode picture can be limited in its applicability to this system. As an alternative, one can develop a travelling-wave picture and transfer (or scattering) matrix approach that incorporates all modes of the fibre system, giving an improved model of the transmission properties . A drawback of the transfer matrix approach is that it is linear and only appropriate for weak coherent driving. In order to have a fully quantum description, we have implemented a numerical method based on tensor-networks, which handles the two-way cascade represented by the connecting fibre in a similar fashion to a coherent time-delayed feedback system . In this presentation I will sum up the experimental results and theoretical methods described above.