Theory of multiqubit superradiance in a waveguide in the presence of finite delay times and two quantum excitations

We study the quantum nonlinear dynamics of multiple two-level atoms (qubits) in a waveguide quantum electrodynamics system, with a focus on modified superradiance effects between two or four atoms with finite delay times. Using a numerically exact matrix-product-states approach, we explore both Markovian and non-Markovian regimes and highlight the significant influence of time-delayed feedback effects and the clear breakdown of assuming instantaneous coupling dynamics. We first show a system composed of two spatially separated qubits, prepared in a doubly excited state (both fully excited), and provide a comprehensive study of how delayed feedback influences the collective system decay rates, as well as the quantum correlations between waveguide photons, atoms, and between atoms and photons. The system is then extended to include two additional qubits located next to the initial ones (four qubits in total), and we demonstrate, by manipulating the initial excitations and the time-delay effects, how long-term quantum correlations and light-matter entangled states can be established.