Active Quantum State Purification and Nonlinear-Order Filtering via Longitudinal Light Drag in Four-Wave Mixing

In electromagnetically induced transparency (EIT) media, the generation of highly pure quantum squeezed states via four-wave mixing (FWM) is fundamentally limited by co-propagating higher-order nonlinearities. These processes shear the quantum phase space and couple anti-squeezed noise into the measurement axis, destroying quantum correlations. Here, we theoretically propose an active, completely collinear quantum state purification paradigm utilizing the longitudinal Fresnel-Fizeau light drag effect. By establishing a fully coupled continuous-variable quantum electrodynamic model, we reveal that the moving EIT medium acts as an intrinsic nonlinear-order low-pass filter. Crucially, higher-order susceptibilities obey a significantly steeper inverse-power-law dependence on the drag-induced Doppler shift compared to the fundamental FWM. The giant macroscopic phase mismatch scales with the number of interacting slow-light photons. This dual-scaling mechanism creates an optimal ultra-slow velocity window (e.g., [Formula: see text] 0.05 mm/s ) where fifth-order excess phase noises are exponentially quenched while the third-order parametric squeezing survives. Our results demonstrate the deterministic recovery of deep squeezed vacuum from noise-dominated thermal states, providing a non-invasive kinematic method for macroscopic quantum state engineering and precision atom-light interfaces.