A Theoretical and Experimental Study of Quantum Coherence Effects in Nigerian Mineral Fluorite Crystal Structures Under Optical Excitation

Quantum coherence phenomena in rare-earth ion-doped fluorite crystal hosts have become a focus of intensive research for applications in quantum information processing, optical quantum memory, and precision metrology. Fluorite mineral specimens from Nigeria's basement complex in Kaduna and Niger States contain natural impurities including europium, dysprosium, and erbium ions substituted into calcium fluoride host sites, making them candidate materials for study of quantum coherence without the cost of synthetic crystal growth. This research theoretically and experimentally investigates quantum coherence properties, dephasing mechanisms, and spectral hole burning characteristics of naturally occurring fluorite samples from Nigerian mineral sources. A theoretical model of decoherence in rare-earth-doped fluorite is developed using the Lindblad master equation formalism, incorporating phonon bath, nuclear spin flip-flop, and charge noise dephasing channels with parameters derived from first-principles lattice dynamics calculations using density functional perturbation theory. Experimentally, photon echo and free induction decay transient spectroscopy measurements were performed using a tunable narrow-linewidth cw laser and acousto-optic modulator pulse sequencing at liquid helium temperature. Optical coherence lifetime T2 values up to 4.2 microseconds were measured in europium-doped specimens, and spectral hole widths of 680 Hz were recorded, indicating the material's potential for spectral hole burning memories. Original contributions include derivation of modified spectral diffusion rate expressions for the low-impurity-concentration regime applicable to natural mineral fluorite and experimental demonstration of magnetically decoupled coherence lifetime extension. Keywords: quantum coherence, fluorite, rare-earth ions, photon echo, optical quantum memory