Tunable Entanglement of Multi-Level Atoms in Photonic Crystals: Leveraging Resonant Dipole Interactions and Quantum Interference

We present a comprehensive investigation of entanglement dynamics in multi-level V-type atomic systems embedded within PC cavities. We mainly focus on the synergistic roles of resonant dipole-dipole interactions and quantum interference through analytical modeling and numerical simulations using the Schrodinger equation. In our analysis, we show that resonant dipole-dipole interactions and quantum interference serve as potent tools for tuning and stabilizing entanglement in structured photonic environments. Key findings reveal that resonant interaction dominates when interatomic distances align with the localization length of photonic bound states induced by bandgap which enables coherent coupling via evanescent fields. The entanglement is preserved for extended times when dipoles of each atom are aligned parallel or anti-parallel while a novel oscillatory entanglement mechanism emerges from orthogonally aligned atomic dipoles. It is mainly driven by destructive interference between vacuum-mediated pathways and bandgap-engineered photonic density of states. This mechanism exhibits non-Markovian dynamics, including delayed feedback and entanglement revival. We further demonstrate that positioning the atomic excited states deeper within the photonic bandgap accelerates the decay of entanglement oscillations due to the exponential suppression of resonant energy exchange mediated by evanescent modes.