Pump-Induced Biphasic Relaxation Model of Xe Spin in Nuclear Magnetic Resonance Gyroscopes

The spin relaxation rate of Xe isotopes is a key characteristic of nuclear magnetic resonance gyroscopes (NMRGs). A pump-induced biphasic relaxation (PBR) model is proposed to describe the pump dependence of the transverse relaxation rate of ¹²⁹Xe nuclear spin. The distribution of electron polarization is theoretically analyzed based on the Bloch-Torrey equations and the volume-averaged polarization is evaluated through NMR frequency shift measurements. Experimental results confirm the theoretical quadratic dependence between Γ and PRb with a high fitting accuracy (R² = 0.9969). The predicted linear (R² > 0.9966) and hyperbolic (R² > 0.9942) regimes of Γ versus pump power are also observed. Validation across different pump power conditions shows agreement between the model and measurements, with an average relative deviation of 0.2169%. The multi-stage process of nuclear spin relaxation is quantified, thereby providing a robust validation for the PBR model.