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arXiv:2607.10083

Unified Phase-Space Mapping of Quantum Observables in a Multi-Driven Vapor: Resonance Fluorescence as an Electrometry Probe and Correlation Witness

M. S. Ateto, Emad K. Jaradat, S. M. Abo-Dahab

quant-phSubmitted Jul 11, 2026• Announced Jul 14, 2026• 0 citations
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Abstract

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.

Comments
23 pages, 9 figures

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Europhysics Letters (EPL)•May 1, 2007•8 citations
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.
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We present a unified, geometry-resolved framework for absorption, resonance fluorescence, entanglement, and phase-space quasiprobability in Doppler-broadened four-level Rydberg atoms. Within a density-matrix formalism incorporating velocity averaging and dressed-state analysis, these observables are shown to constitute complementary projections of a common coherence-driven structure governed by multi-photon interference. We further introduce the Stratonovich-Weyl (SW) Wigner function as a phase-space representation that encodes both population and coherence contributions on equal footing. A direct comparison reveals a near one-to-one correspondence between SW quasiprobability structures and entanglement landscapes, with coherence-induced features such as avoided crossings and detuning-dependent ridges preserved across representations. Isolating the Doppler-odd component yields an eigenvalue-free proxy that captures the same coherence geometry underlying entanglement negativity. Resonance fluorescence emerges as a thermally robust and experimentally accessible observable: unlike absorption, it preserves spectral structure under Doppler averaging and reliably tracks dressed-state dynamics and entanglement extrema. Strong-field dressing and propagation geometry control the redistribution of coherence across velocity classes, leading to characteristic spectral asymmetries and ridge formation. These results establish a direct link between phase-space structure, spectroscopic observables, and quantum correlations in thermal media. By combining a coherence-resolved description with a Doppler-sensitive phase-space representation, this framework provides an experimentally accessible route for entanglement characterization without eigenvalue reconstruction, enabling Doppler-resilient, fluorescence-based quantum sensing in warm Rydberg systems.
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We investigate Degenerate Four-Wave Mixing (DFWM) in a thermal cesium vapor using a nearly collinear, co-propagating geometry under deeply non-perturbative conditions (I≈150Is). While standard theoretical treatments that coherently average over the atomic velocity distribution predict a pronounced spectral dip at resonance, our experimental measurements consistently exhibit a single, smooth, Doppler-broadened profile. To resolve this discrepancy, we develop a non-perturbative theoretical model based on a spatial harmonic expansion of the optical Bloch equations, replacing the standard coherent integration with an incoherent summation over velocity classes. By combining this incoherent velocity averaging with a Beer-Lambert attenuation correction, our model accurately reproduces both the experimentally observed smooth spectral line shape and the sublinear power dependence characteristic of highly saturated multi-photon processes. These results suggest that non-homogeneous spatial dephasing processes in dense, highly saturated thermal media play an important role in the dynamics of the interaction.
We investigate an inhomogeneously broadened four-level atomic system driven by two strong coherent fields and probed by a weak laser. By carefully adjusting strengths of the driving fields, we can observe a greatly enhanced peak between two dark resonances in the probe absorption spectrum. The enhanced absorption peak will split into two lower ones and then result in a third dark resonance if we gradually weaken one driving field. Ultimately, the whole probe absorption spectrum evolves towards the usual EIT spectrum with only one dark resonance. Based on appropriate numerical calculations and qualitative analysis, we show that the experimental results can be well understood by separately considering the probe absorptions arising from partial atoms with different velocities.