Moiré superradiance in cavity quantum electrodynamics with quantum atom gas

As a novel platform for exploring exotic quantum phenomena, the moir\'e lattice has garnered significant interest in solid-state physics, photonics, and cold-atom physics. While moir\'e lattices in two- and three-dimensional systems have been proposed for neutral cold atoms, the simpler one-dimensional moir\'e effect remains largely unexplored. We present a scheme demonstrating moir\'e effects in a one-dimensional cold-atom--cavity coupling system, which resembles a generalized open Dicke model exhibiting superradiant phase transitions. We reveal a strong link between the phase transition critical point and the one-dimensional moir\'e parameter. Evidence of the one-dimensional moir\'e effect is explicitly explored, including the cavity field spectrum, phase transition dynamics, and anomalous atomic diffusion. This work provides a new route for testing one-dimensional moir\'e effects with cold atoms and opens new possibilities in moir\'e metrology.