  We theoretically study the single photon transport properties in periodic and
position-disordered Jaynes-Cummings (or JC) arrays of waveguide-coupled
microtoroidal ring resonators, each interacting with a single two-level quantum
emitter. Employing the real-space formalism of quantum optics, we focus on
various parameter regimes of cavity quantum electrodynamics (cQED) to gain
better control of single photon propagation in such a many-body quantum optical
setting. As for some of the key findings, we observe that the periodic setting
leads to the formation of the band structure in the photon transmission
spectra, which is most evident in the strong coupling regime of cQCD. However,
under the resonant conditions with no losses, the application of Bloch's
theorem indicates that the width of forbidden gaps can be altered by tuning the
emitter-cavity coupling to small values. Moreover, in the disordered case, we
find that the single photon transmission curves show the disappearance of band
formation. However, spectral features originating from cQED interactions
observed for single atom-cavity problem remain robust against weak-disordered
conditions. The results of this work may find application in the study of
quantum many-body effects in the optical domain as well as in different areas
of quantum computation and quantum networking.
