Fluorescence as A Qualitative Electrometry Readout and Entanglement Indicator with A Stratonovich-Weyl Wigner Calibration Framework for Moving 4-Level Rydberg Atoms
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.
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.
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.
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.
We investigate a four-level Rydberg atom in the V+ Θ configuration using the master equation formalism under a weak probe approximation. Analytical solutions for steady-state coherences reveal how control-field induced dressed states govern three key observables: resonance fluorescence, entanglement, and electromagnetically induced transparency (EIT). We show that fluorescence spectra encode the same interference pathways responsible for EIT, enabling fluorescence to serve as a robust alternative probe for Rydberg electrometry. Moreover, since fluorescence and subsystems’ entanglement derive from the same density-matrix coherences, spectral sidebands map directly onto peaks in entanglement, making fluorescence an experimentally accessible entanglement witness. A Stratonovich–Weyl Wigner function (SW) provides a unifying perspective: its negative regions, arising from interference-induced coherences, coincide with regimes of enhanced fluorescence and entanglement, establishing it as a general nonclassicality witness. This four-fold correspondence highlights the central role of dressed-state coherences in linking spectroscopy, electrometry, quantum correlations, and nonclassicality. Our work establishes a coherent mathematical framework for interpreting fluorescence as a complementary (and in certain regimes alternative) probe to EIT-based electrometry, as well as an experimentally accessible proxy for entanglement detection and nonclassicality.
We develop a general dressed-state framework for computing fluorescence spectra, probe absorption spectra, and photon-photon correlations of light scattered by ensembles of Nat two-level atoms with arbitrary Jg→Je transitions driven by intense coherent fields. The approach employs a full vectorial treatment of the electromagnetic field, handles any atomic geometries, illumination directions, and polarizations, and yields optical observables as explicit sums of Lorentzian lines whose positions, widths, and weights are directly tied to the eigenvalues and eigenvectors of the Lindbladian. The framework is implemented in an open-source Python package and benchmarked against exact single- and two-atom calculations. We identify geometries in which the full vectorial description is essential, and the scalar approximation fails qualitatively. Applying the method to pairs of atoms with a Jg=0→Je=1 transition, we show that elastic and inelastic scattered intensities collapse onto universal master curves controlled by a single collective saturation parameter built from the dominant superradiant mode, across several orders of magnitude in drive strength and interatomic distance. We identify collective phenomena that require a description beyond this single-mode picture. Extending the analysis to atoms with ground-state degeneracy, we find that most collective features carry over, while two qualitatively new effects emerge: an incoherent spontaneous Raman channel that modifies the scaling of inelastic emission, and a slow timescale in the time-delayed correlations g(2)(τ) governed by the competition between Raman scattering and subradiant decay, controlled by a single dimensionless parameter. These results provide both physical insight and practical computational tools for engineering collective optical responses in few-atom systems such as optical tweezer arrays.
Spectroscopic measurements of single-particle spectral functions provide crucial insight into strongly correlated quantum matter by resolving the energy and spatial structure of elementary excitations. Here we introduce a spectroscopic protocol for single-charge injection with simultaneous spatial and energy resolution in a Rydberg tweezer array, effectively emulating scanning tunneling microscopy. By combining this protocol with single-atom-resolved imaging, we go beyond conventional spectroscopy by not only measuring the single-particle spectral function but also directly imaging the microscopic structure of the excitations underlying spectral resonances in frustrated tJ Hamiltonians. We reveal resonances associated with the formation of bound magnetic polarons -- composite quasiparticles consisting of a mobile hole bound to a magnon -- and directly extract their binding energy, spatial extent, and spin character. Finally, by exploiting the spatial tunability of our platform, we measure the local density of states across different lattice geometries. Our work establishes Rydberg tweezer arrays as a powerful platform for spectroscopic studies of strongly correlated models, offering microscopic control and direct real-space access to emergent quasiparticles in engineered quantum matter.
Abstract We present a first-principles density-matrix simulation of blackbody-radiation (BBR)-induced decoherence in cesium Rydberg electromagnetically induced transparency (EIT). The model incorporates spontaneous emission, blackbody-stimulated transitions, collisional broadening, transit-time-limited decoherence, and Doppler averaging across a truncated but converged Rydberg manifold within a Lindblad masterequation framework. From the steady-state solution, we extract both the temperaturedependent Rydberg coherence decay rate and the corresponding probe absorption coefficient.We show that the experimentally observed modification of probe transmission reported by Kaur et al. (2026) arises predominantly from BBR-induced decoherence of the Rydberg coherence, rather than from population redistribution among Rydberg levels. The model reproduces the observed temperature-dependent trends in probe absorption with quantitative accuracy. By employing a fully m j -resolved transition network, we establish a direct connection between microscopic decoherence processes and macroscopic optical observables. The decoherence effect on the optical response is sufficiently well-defined to serve as a measurable signal, enabling potential applications in Rydberg-based thermometry and radiometry.These results provide a self-consistent microscopic description of BBR-limited performance in thermal-vapor Rydberg EIT and establish a quantitative link between Rydberg-state decoherence and measurable changes in optical susceptibility, with direct relevance to RF-based sensing platforms.