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arXiv:2501.19356 · Physical Review Letters

Addressing the Correlation of Stokes-Shifted Photons Emitted from Two Quantum Emitters

Adrián Juan-Delgado, Jean-Baptiste Trebbia, Rubén Esteban, Quentin Deplano, Philippe Tamarat, Rémi Avriller, Brahim Lounis, Javier Aizpurua

Published Sep 18, 2025• 3 citations
arXivHTMLPDF

Abstract

In resonance fluorescence excitation experiments, light emitted from solid-state quantum emitters is typically filtered to eliminate the laser photons, ensuring that only red-shifted Stokes photons are detected. However, theoretical analyses of the fluorescence intensity correlation often model emitters as two-level systems, focusing on light emitted exclusively from the purely electronic transition (the zero-phonon line), or they rely on statistical approaches based on conditional probabilities that neglect the quantum coherence between the emitters and the coherence between the electric fields they generate. Here, we propose a model to characterize the correlation of either zero-phonon line photons or Stokes-shifted photons. This model successfully reproduces the experimental correlation of Stokes-shifted photons emitted from two interacting molecules and predicts that this correlation is affected by quantum coherence. Besides, we analyze the role of quantum coherence in the Stokes-shifted emission from two distant emitters, showing a sharp peak at zero time delay due to the Hanbury Brown-Twiss effect.

DOI
10.1103/1z52-p73t

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In resonance fluorescence excitation experiments, light emitted from solid-state quantum emitters is typically filtered to eliminate the laser photons, ensuring that only red-shifted Stokes photons are detected. However, theoretical analyses of the fluorescence intensity correlation often model emitters as two-level systems, focusing on light emitted exclusively from the purely electronic transition (the zero-phonon line), or they rely on statistical approaches based on conditional probabilities that neglect the quantum coherence between the emitters and the coherence between the electric fields they generate. Here, we propose a model to characterize the correlation of either zero-phonon line photons or Stokes-shifted photons. This model successfully reproduces the experimental correlation of Stokes-shifted photons emitted from two interacting molecules and predicts that this correlation is affected by quantum coherence. Besides, we analyze the role of quantum coherence in the Stokes-shifted emission from two distant emitters, showing a sharp peak at zero time delay due to the Hanbury Brown-Twiss effect.
Resonance fluorescence of a two-level emitter displays persistently anti-bunching irrespective of the excitation intensity, but inherits the driving laser’s linewidth under weak monochromatic excitation. These properties are commonly explained in terms of two disjoined pictures, i.e., the emitter’s single photon saturation or passively scattering light. Here, we propose a unified model that treats all fluorescence photons as spontaneous emission, one at a time, and can explain simultaneously both the spectral and correlation properties of the emission. We theoretically derive the excitation power dependencies, measurable at the single-photon incidence level, of the first-order coherence of the whole resonance fluorescence and super-bunching of the spectrally filtered, followed by experimental confirmation on a semiconductor quantum dot micro-pillar device. Furthermore, our model explains peculiar coincidence bunching observed in phase-dependent two-photon interference experiments. Our work provides an intuitive understanding of coherent light-matter interaction and may stimulate new applications. Standard descriptions of resonance fluorescence consider either absorption and re-emission in a single-photon picture or passive scattering. This study shows that resonance fluorescence can be described by a pure quantum state of the emitter and photon, revealing a coherent superposition that challenges the conventional view of spontaneous emission as an incoherent process.
The interaction between quantum emitters leads to the formation of superradiant and subradiant states with possible applications in quantum technologies. To improve the characterization of light emission from these systems, we present here a systematic theoretical analysis of the intensity correlation from two strongly interacting quantum emitters at cryogenic temperatures as a function of the frequency and intensity of the excitation laser. This analysis effectively accounts for the effect of vibrational modes of the emitters and of phonons of the environment through the combined Debye-Waller/Franck-Condon factor. First, we analyze the color-blind intensity correlation and show that it can be tailored from strong antibunching to strong bunching by tuning the laser from the two-photon resonance to the transition frequency of the superradiant state. We also find a particularly complex behavior of the intensity correlation when the laser frequency is tuned to that of the transition of the subradiant state, giving raise to the possibility of emitting bunched and antibunched light depending on the laser intensity and the detuning between the two emitters. The numerical results are supported by analytical equations that can be used for the experimental characterization of the interacting emitters. Additionally, by selecting photons of particular frequencies, we analyze the rich landscape of frequency-resolved intensity correlations, which also depend on the laser detuning and intensity. The analysis of the frequency-resolved correlations provides further information about the different relaxation processes underlying the photon emission, unveiling one-photon and two-photon emission processes that cannot be resolved neither in the emission spectrum nor in the color-blind intensity correlation. These results show that two interacting emitters are a versatile and practical source of quantum light and highlight the usefulness of the intensity correlation to unveil complex dynamics in this system. Published by the American Physical Society 2024
Resonance fluorescence arises from the coherent interaction of laser light with a two-level system and constitutes a quantum light source exhibiting single-photon emission and antibunching, making it a fundamental building block for future quantum networks. Our recent work [Nat. Commun.16, 6453 (2025)10.1038/s41467-025-61884-x] demonstrates that under continuous-wave excitation and in the absence of pure dephasing, the single-time joint state of resonance fluorescence and the two-level system can be described by a pure entangled state. Here, we analyze the cross-correlation and auto-correlation properties of the quantum optical field generated by the interference of resonance fluorescence with laser light at the resonance excitation frequency. Simulation results indicate that by varying the intensity or phase of the interfering laser light, the higher-order coherence of the post-interference quantum optical field transitions from anti-bunching to super-bunching behavior, consistent with recent theoretical and experimental advances by mean-field engineering. This approach offers a complementary framework to characterize and manipulate the multiphoton quantum optical fields.
Resonance fluorescence has played a major role in quantum optics with predictions and later experimental confirmation of nonclassical features of its emitted light such as antibunching or squeezing. In the Rayleigh regime where most of the light originates from the scattering of photons with subnatural linewidth, antibunching would appear to coexist with sharp spectral lines. Here, we demonstrate that this simultaneous observation of subnatural linewidth and antibunching is not possible with simple resonant excitation. Using an epitaxial quantum dot for the two-level system, we independently confirm the single-photon character and subnatural linewidth by demonstrating antibunching in a Hanbury Brown and Twiss type setup and using high-resolution spectroscopy, respectively. However, when filtering the coherently scattered photons with filter bandwidths on the order of the homogeneous linewidth of the excited state of the two-level system, the antibunching dip vanishes in the correlation measurement. Our observation is explained by antibunching originating from photon-interferences between the coherent scattering and a weak incoherent signal in a skewed squeezed state. This prefigures schemes to achieve simultaneous subnatural linewidth and antibunched emission.
Quantum optics provides a fundamental framework for understanding the interaction between light and matter at the quantum level. Recently, it has been shown that under incoherent pumping, the resonance fluorescence spectrum dramatically changes. Engineering the resonance fluorescence spectrum paves the way towards solid-state-based single-photon sources. In this paper, we start by reviewing and reproducing some of the results concerning the resonance fluorescence spectrum, single-photon sources, dressed-state lasers, and luminescence spectrum of a quantum dot in a microcavity. Photon correlations in quantum optical systems and spectral properties of radiation emitted by atomic and semiconductor systems interacting with external fields are investigated. The well known Mollow triplet structure of the emission spectrum is discussed, together with the role of dressed states in explaining the origin of the three spectral peaks. Furthermore, the luminescence spectra of quantum emitters coupled to microcavities are reviewed. The numerical results presented here contribute to the theoretical understanding of resonance fluorescence, photon correlations, and engineered emission in quantum optical systems. These studies highlight the rich physical properties arising from light matter interaction at the quantum level and demonstrate their relevance for emerging quantum technologies.
Photon-mediated interactions between atoms can arise via coupling to a common electromagnetic mode or by quantum interference. Here, we probe the role of coherence in cooperative emission arising from two distant but indistinguishable solid-state emitters because of path erasure. The primary signature of cooperative emission, the emergence of "bunching" at zero delay in an intensity correlation experiment, is used to characterize the indistinguishability of the emitters, their dephasing, and the degree of correlation in the joint system that can be coherently controlled. In a stark departure from a pair of uncorrelated emitters, in Hong-Ou-Mandel-type interference measurements, we observe photon statistics from a pair of indistinguishable emitters resembling that of a weak coherent state from an attenuated laser. Our experiments establish techniques to control and characterize cooperative behavior between matter qubits using the full quantum optics toolbox, a key step toward realizing large-scale quantum photonic networks.