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

Abstract

We present a comprehensive investigation of entanglement dynamics in multi-level V-type atomic systems embedded within photonic crystals. 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. Key findings reveal that resonant interaction dominates when the interatomic distance is comparable to the localization length of photon-atom bound states lying in the bandgap region. For atoms with anti-parallel dipole orientations, both initially entangled and separable states exhibit robust entanglement preservation due to strong collective interactions. Conversely, when dipoles are oriented orthogonally, initially entangled states exhibit unique oscillatory patterns in their entanglement dynamics. This effect arises from the formation of dark states due to destructive interference within the structured photonic environment, with resonant dipole-dipole interactions sustaining non-Markovian dynamics. 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. Our analysis establishes resonant dipole-dipole interactions and quantum interference as potential tools for tailoring entanglement dynamics, paving the way for controlled quantum coherence in photonic crystal platforms.