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arXiv:2412.09252 · Nature Communications

Cavity-mediated collective emission from steady-state subradiance

Kyu-Young Kim, Jinhee Lee, Woong Bae Jeon, Dong Hyun Park, Suk In Park, Jin Dong Song, Changhyoup Lee, Je‐Hyung Kim

Published Jul 9, 2025• 10 citations
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Abstract

Cooperative effects such as super(or sub)radiance in quantum systems arise from the interplay among quantum emitters. While bright superradiant states have been extensively studied and have yielded important insights into cooperative phenomena, subradiant states remain less explored due to their inherently dark state nature. However, subradiance holds significant potential as a valuable quantum resource exploiting long-lived and large-scale entanglement, which is a key for advancing quantum information technologies. Here, we demonstrate strong collective emission from a cavity-mediated steady-state subradiant state. In a tailored photonic environment with balanced cavity dissipation, emitter-field coupling strength, and incoherent pumping, two quantum dots coupled to a low-Q cavity exhibit a steady-state population in a subradiant state with a highly negative cooperativity parameter among the emitters. As a key signature of steady-state subradiance, the system shows strong photon bunching ( $${{{\rm{g}}}}^{\left(2\right)}\left(0\right) > 8$$ ) and suppressed single-photon decay (36 ns). Furthermore, we investigate that such collective interactions can be manipulated by controlling various system parameters, such as detuning and dephasing, supported by numerical simulations. Our approach to inducing cavity-mediated subradiance paves the way for generating and harnessing quantum correlations among quantum emitters via controlled dissipation. Subradiance is a cooperative effect in systems of quantum emitters, which is the opposite of superradiance, or enhanced emission, but has been less explored. Here, the authors demonstrate a steady-state subradiant state in a system of two InAs quantum dots coupled to a low-Q nanophotonic cavity.

DOI
10.1038/s41467-025-61629-w

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Cooperative effects such as super(or sub)radiance in quantum systems arise from the interplay among quantum emitters. While bright superradiant states have been extensively studied and have yielded important insights into cooperative phenomena, subradiant states remain less explored due to their inherently dark state nature. However, subradiance holds significant potential as a valuable quantum resource exploiting long-lived and large-scale entanglement, which is a key for advancing quantum information technologies. Here, we demonstrate strong collective emission from a cavity-mediated steady-state subradiant state. In a tailored photonic environment with balanced cavity dissipation, emitter-field coupling strength, and incoherent pumping, two quantum dots coupled to a low-Q cavity exhibit a steady-state population in a subradiant state with a highly negative cooperativity parameter among the emitters. As a key signature of steady-state subradiance, the system shows strong photon bunching ( g(2)(0)>8{{{\rm{g}}}}^{\left(2\right)}\left(0\right) > 8g(2)(0)>8 ) and suppressed single-photon decay (36 ns). Furthermore, we investigate that such collective interactions can be manipulated by controlling various system parameters, such as detuning and dephasing, supported by numerical simulations. Our approach to inducing cavity-mediated subradiance paves the way for generating and harnessing quantum correlations among quantum emitters via controlled dissipation. Subradiance is a cooperative effect in systems of quantum emitters, which is the opposite of superradiance, or enhanced emission, but has been less explored. Here, the authors demonstrate a steady-state subradiant state in a system of two InAs quantum dots coupled to a low-Q nanophotonic cavity.
Cooperative phenomena, such as super(sub)radiance in quantum systems, arise from interactions among quantum emitters. Superradiance has been intensively studied from various platforms. While superradiance provides a good insight into the collective effect in quantum systems, exploiting the entangled state is not easy because of its strong radiative nature. In contrast, subradiance remains largely unexplored due to its inherent dark nature, despite its long lifetime and robustness against dephasing. Here, we experimentally demonstrate a long-lived subradiance among multiple quantum dots coupled to a low-Q cavity. The directional cavity mode provides a constant momentum condition, similar to a waveguide, and facilitates a shared radiative field among the quantum dots. By balancing cavity dissipation, incoherent pumping, and coupling strength, we realize steady-state subradiance rather than superradiance. As a key signature of subradiance, we observe a stark change in the photon statistics, with photon bunching exceeding the classical limit of 2. Additionally, we engineer the coupled system by changing detuning and incoherent pumping. Furthermore, modifying the pumping mechanism allows us to manipulate the dephasing of quantum dots involved in the cooperative process. Our experimental study on cavity-mediated cooperative phenomena among multiple quantum dots introduces a novel approach to generating quantum correlations with long-lived entanglement, offering potential applications in quantum storage and metrology.
The Tavis–Cummings system, wherein emitters collectively interact with the same optical mode, has been a long-standing model to study collective photon emission phenomena such as superradiance. However, disorder in the resonant frequencies of the quantum emitters can perturb these effects. In this paper, we study the impact of dynamic modulation on the interplay between superradiance and spectral disorder. Through numerical simulations and analytical calculations, we provide evidence that the effective cooperativity of the superradiant mode can be multiplicatively enhanced with a quantum control protocol modulating the resonant frequency of the optical mode. Our results are relevant to experimental demonstration of superradiance in solid-state quantum optical systems, wherein the spectral disorder is a signficant technological impediment toward achieving photon-mediated emitter–emitter couplings.
We theoretically investigate the emission properties of a single-mode cavity coupled to a mesoscopic number of incoherently pumped quantum emitters. We propose an operational measure for the medium cooperativity, valid both in the bad- and in the good-cavity regimes. We show that the opposite regimes of subradiance and super-radiance correspond to negative and positive cooperativity, respectively. The lasing regime is shown to be characterized by non-negative cooperativity. In the bad-cavity regime we show that the cooperativity defines the transitions from subradiance to super-radiance. In the good-cavity regime it helps to define the lasing threshold, also providing distinguishable signatures indicating the lasing regime. Increasing the quality factor of the cavity mode induces a crossover from the solely super-radiant to the lasing regime. Furthermore, we verify that lasing is manifested in a wide range of positive cooperative behavior, showing that stimulated emission and super-radiance can coexist. The robustness of the cooperativity is studied with respect to experimental imperfections, such as inhomogeneous broadening and pure dephasing.
We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well-distinguished statistical properties of the emitted radiation. For small cavity decay rates, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared with the emitter–cavity coupling) and for a few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady-state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows us to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-the-art techniques of Q -switch of resonant cavities, allied with the recent capability of tuning single emitters in and out of resonance, suggest this system to be a versatile source of different quantum states of light.
The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.
Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity CCC, the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, CCC is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work [Phys. Rev. Lett. 119, 093601 (2017)], we have shown that collective excitations in ensembles of dipole-dipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavity-emitter system's collective Kerr nonlinear effect.