Simulating topological effects with photons in coupled QED cavity arrays

We provide a pedagogical account of an early proposal realizing fractional quantum Hall effect (FQHE) using coupled quantum electrodynamics (QED) cavity arrays (CQCAs). We start with a brief introduction on the basics of quantum Hall effects and then review the early proposals in the simulation of spin-models and fractional quantum Hall (FQH) physics with photons in coupled atom-cavity arrays. We calculate the energy gap and the overlap between the ground state of the system and the corresponding Laughlin wavefunction to analyze the FQH physics arising in the system and discuss possibilities to reach the ground state using adiabatic methods used in Cavity QED.