Unified Phase-Space Mapping of Quantum Observables in a Multi-Driven Vapor: Resonance Fluorescence as an Electrometry Probe and Correlation Witness
We present a unified, geometry-resolved framework for analyzing absorption, resonance fluorescence, entanglement negativity, and phase-space quasiprobability in Doppler-broadened four-level atomic vapor. Using a density-matrix formalism with thermal velocity averaging and exact dressed-state diagonalization, we show that these observables constitute complementary projections of a common coherence-driven phase-space structure governed by multiphoton interference. Central to this framework is the Stratonovich-Weyl (SW) Wigner function, which provides a unified phase-space representation incorporating both populations and coherences. Direct comparison reveals a near one-to-one correspondence between SW quasiprobability distributions and entanglement landscapes, with geometry-dependent features, including hyperbolic dispersion asymptotes and split resonance ridges, consistently preserved. Furthermore, isolating the Doppler-odd component yields an eigenvalue-free proxy that captures the coherence geometry underlying entanglement negativity, providing a non-invasive quantum correlation witness. At the same time, resonance fluorescence emerges as a thermally robust observable: unlike susceptibility-based absorption, its additive pole weighting preserves sharp Autler-Townes spectral features under strong driving. This robustness enables fluorescence to accurately track bright dressed states and entanglement extrema despite severe Doppler dephasing, establishing its dual role as a sensitive electrometry probe and correlation witness. By combining a coherence-resolved description with a Doppler-sensitive phase-space representation, the proposed framework offers an experimentally accessible, eigenvalue-free approach to quantum state characterization, enabling Doppler-resilient fluorescence-based quantum sensing and precision field electrometry in warm atomic media.