Single-photon transport properties in periodic and position-disordered coupled atom-cavity arrays

We analyze the transport properties of single photons in one-dimensional lattices of a waveguide-coupled atom-cavity system [arXiv:2401.15231]. By investigating various parameter regimes, we find that when atoms are decoupled from the cavities or are coupled (either weakly or strongly), the transmission and reflection spectra exhibit the formation of a frequency comb pattern. In particular, in the strong coupling regime, these frequency combs are superimposed on the frequency doublet spectrum originating from the Rabi splitting. We further took the infinitely long extension of the setup. We study the photonic dispersion properties, which we found to be engineerable through the atom-cavity detuning, cavity backscattering, and strong coupling regime of cavity quantum electrodynamics. Finally, when the cavities' position (microring resonators in our model) is subjected to disorder, obeying a Gaussian distribution, we find that the frequency combs are smoothed over and that the general single atom-cavity spectral behavior becomes dominant. The study of quantum many-body physics in optical systems and quantum networking can be the two targeted areas of application of this work.