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Physical Review Research

Tailoring the statistics of light emitted from two interacting quantum emitters

Adrián Juan-Delgado, Rubén Esteban, Álvaro Nodar, Jean-Baptiste Trebbia, Brahim Lounis, Javier Aizpurua

Published May 24, 2024• 11 citations
Publisher

Abstract

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

DOI
10.1103/physrevresearch.6.023207

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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
Two nonidentical quantum emitters, when placed within a cavity and coherently excited at the two-photon resonance, can reach stationary states of nearly maximal entanglement. In Vivas-Viaña, Martín-Cano, and Sánchez Muñoz [], we introduce a frequency-resolved Purcell effect stabilizing entangled W states among strongly interacting quantum emitters embedded in a cavity. Here we delve deeper into a specific configuration with a particularly rich phenomenology: two interacting quantum emitters under coherent excitation at the two-photon resonance. This scenario yields two resonant cavity frequencies where the combination of two-photon driving and Purcell-enhanced decay stabilizes the system into the subradiant and superradiant states, respectively. By considering the case of nondegenerate emitters and exploring the parameter space of the system, we show that this mechanism is merely one among a complex family of phenomena that can generate both stationary and metastable entanglement when driving the emitters at the two-photon resonance. We provide a global perspective of this landscape of mechanisms and contribute analytical characterizations and insights into these phenomena, establishing connections with previous reports in the literature and discussing how some of these effects can be optically detected. Published by the American Physical Society 2024
We investigate two-color photon correlations in the light emitted by two strongly driven, strongly interacting two-level emitters. The correlations are interpreted introducing the collective dressed states picture, which allows us to describe both bunching and antibunching based on the allowed and prohibited transitions. At odds from weakly interacting emitters, the strong interaction lifts the degeneracy of the energy differences between the different states, leading to a temporal breaking of symmetry for the correlations: photons of different frequencies may not be emitted in any order. Finally, we show that most of the virtual processes, which involve pairs of photons, yield nonclassical correlations when the sum of their energies fits any of the interaction-induced sidebands in the emitted spectrum. In particular, depending on the frequency of the emitted photons, correlations strong enough to violate Bell inequalities can appear.
Accessing complete information about the emission from any quantum-optical systems requires tools capable of a frequency-resolved characterization of multi-photon transitions that would go beyond the standard g(2) correlation measurements. This is particularly important when analyzing systems which exhibit strong nonlinear response with multiple emission pathways. In this work, we calculate and analyze in details correlations of light emitted from two such canonical nonlinear optical systems, one incorporating Kerr nonlinear medium, and another exhibiting optomechanical coupling between light and quantized motion of a generic mechanical oscillator. We compare their single- and two-photon emission characteristics by employing a recently developed framework that allows us to calculate the frequency-resolved g(2) correlations between emitted photons with two arbitrary frequencies. Our analysis shows a rich landscape of bunching and antibunching associated with multi-photon emission events, and reveals the distinctive temporal characteristics of such processes. This new understanding provides a new asset to characterize and exploit nonlinear phenomena in Kerr and optomechanical systems in future experiments.
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.
Frequency-resolved photon emission is central to applications from quantum information encoding to high-resolution spectroscopy, and then studying their correlations is therefore essential for revealing the underlying emission pathways and multiphoton statistics. Here, we investigate frequency-resolved N-photon correlations in an ultrastrongly coupled cavity QED system where a qubit interacts with a single-mode cavity. Owing to counter-rotating interactions, the eigenstates and energy spectrum are strongly modified, giving rise to rich spectral and statistical properties in the emitted frequency-resolved photons. Through frequency-selective detection, we reveal pronounced multiphoton antibunching, as well as multiphoton bunching originating from cascade transitions among dressed eigenstates. In particular, we show that parity symmetry plays a decisive role in shaping these correlations. The symmetry-breaking opens additional transition channels and dramatically enhances the generation of correlated photon pairs and even photon triplets of different frequencies. Our work extends frequency-resolved correlations to the ultra-strong coupling regime and demonstrates their potential as a sensitive probe of symmetry in light-matter interaction systems.
Abstract Frequency-resolved photon statistics of resonance fluorescence generated from a two-level system driven by a strong laser field and a weak laser field with equal frequencies are studied. The frequency resolution of fluorescent radiation is described by quantum filtering dynamics, which is simulated theoretically by two single-mode quantum optical cavities with tunable frequencies to scan the incident fluorescent radiation. By calculating the two-photon intensity–intensity correlation functions in terms of the cavity modes, we demonstrate that two-color strong correlations of resonance fluorescence can be generated not only between the opposite sidebands, but also between the central band and one of the sidebands: although both sidebands are broadened due to the perturbation of the weak laser field on the strong-field dressed atom. We emphasize that these properties are in contrast to the conventional case of the standard single-atom Mollow triplet. Moreover, if the resonance frequencies of the two filtering cavities are tuned appropriately, broadband two-color strong correlations are predicted, and the physical origin is revealed from the perspective of quantum interference of photon emission dynamics. This can be considered as a feasible scheme for the design of broadband non-classical light sources, and may be beneficial to the quantum precise detection of atomic and molecular dynamics via quantum optical spectroscopy.