Non‐Markovian Dynamics of Quantum Resources in an Anisotropic Photonic Bandgap Crystal: Metrology and Entanglement

ABSTRACT We study the time evolution of quantum Fisher information and atom–field entanglement for a V‐type three‐level atom embedded in an anisotropic photonic bandgap crystal. The structured reservoir strongly modifies the atomic decay near the photonic bandgap, giving rise to non‐Markovian memory effects. By employing the quantum Fisher information matrix, we determine the quantum Cramér‐Rao bound for both single‐parameter estimation and simultaneous two‐parameter estimation encoded in the atomic initial state. In parallel, we investigate the dynamics of atom‐field entanglement, quantified through the Von Neumann entropy, to characterize the correlations resulting from the interaction with the photonic bandgap. Our results show that both the detuning of the atomic transition frequency from the upper band edge frequency and the initial relative phase play a crucial role in the attainable precision and long‐lived entanglement. These findings demonstrate the potential of photonic bandgap materials as structured reservoirs for protecting quantum information, sustaining long‐time entanglement, and enhancing multiparameter quantum metrology.