我们对嵌入金刚石纳米柱中的氮-空位（NV）发射体进行了强度关联（$g^{(2)}(τ)$）测量。在室温下，我们观察到来自单重态和三重态的跃迁速率均增大了约6倍，表明纳米柱内多个发射体之间存在协同效应。同时，我们观测到$g^{(2)}(0) > 0.5 (\ o 1$)，而其他发射体（以及单个发射体的预期情况）则为$g^{(2)}(0) < 0.5$，这表明体系中至少存在两个发射体。此外，我们观察到$g^{(2)}$呈现三指数行为，这与单个NV发射体所呈现的标准双指数行为形成对比。为了理解我们的实验观测结果，我们建立了一个理论模型。我们求解了针对单个和两个NV中心量身定制的Lindblad主方程，以研究它们在有限温度下耦合到共同电磁场时的耗散动力学。通过这一分析，我们确定双发射体系统的超辐射发射是对所观测数据最可能的解释。我们还发现，使用耦合发射体系统进行的随机数生成在NIST测试套件下表现更好，并用耦合发射体系统的熵驱动模型对此进行了解释。我们的结果为多光子态（例如超辐射态）提供了一种利用强度关联测量的新特征，这将对量子光子技术的进步具有重要意义。
英文摘要：
We perform intensity correlation ($g^{(2)}(τ)$) measurements on nitrogen-vacancy (NV) emitters embedded in diamond nanopillars. We observe an increase in transition rates from both the singlet and triplet states by a factor of $\approx 6$, indicating cooperative effects between the multiple emitters in the pillar, at room temperature. We simultaneously observe a $g^{(2)}(0) > 0.5 (\to 1$) as opposed to $g^{(2)}(0) < 0.5$ for others (and as expected for single emitters), indicating the presence of at least two emitters. Furthermore, we observe a triple exponential behaviour for the $g^{(2)}$ in contrast to the standard double exponential behaviour seen for single NV emitters. To understand our experimental observations, we developed a theoretical model. We solve the Lindblad master equation, tailored for single and two NV centers, to study their dissipative dynamics when coupled to a common electromagnetic field, at a finite temperature. Through this, we identify superradiant emission from a two-emitter system as the most likely explanation for our observed data. We also find that random number generation using the coupled emitter system performs better under the NIST test suite and explain it in terms of an entropy-driven model for a coupled emitter system. Our results provide a new signature for multiphotonic states, such as superradiant states, using intensity correlation measurements, that will become important for quantum photonic technologies progress.
Superradiance is the enhanced emission of photons from quantum emitters collectively coupling to the same optical mode. However, disorder in the resonant frequencies of the quantum emitters can perturb this effect. In this paper, we study the interplay between superradiance and spectral disorder in a dynamically modulated Tavis-Cummings model. Through numerical simulations and analytical calculations, we show that the effective cooperativity of the superradiant mode, which is always formed over an extensive number of emitters, can be multiplicatively enhanced with a quantum control protocol mo…
Sampling methods to describe superradiance in large ensembles of quantum emitters
University of Manchester（曼彻斯特大学）；Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research)（A*STAR材料研究与工程学院）；Newcastle University（纽卡斯尔大学）；Instituto de Estructura de la Materia (IEM), Consejo Superior de Investigaciones Científicas（西班牙国家研究委员会物质结构研究所）
Indistinguishable quantum emitters confined to length scales smaller than the wavelength of the light become superradiant. Compared to uncorrelated and distinguishable emitters, superradiance results in qualitative modifications of optical signals such as photon coincidences. However, recent experiments revealed that similar signatures can also be obtained in situations where emitters are too far separated to be superradiant if correlations between emitters are induced by the wave function collapse during an emission-angle-selective photon detection event. Here, we compare two sources for coop…
Dicke superradiance is an example of emergence of macroscopic quantum coherence via correlated dissipation. Starting from an initially incoherent state, a collection of excited atoms synchronizes as they decay, generating a macroscopic dipole moment and emitting a short and intense pulse of light. While well understood in cavities, superradiance remains an open problem in extended systems due to the exponential growth of complexity with atom number. Here we show that Dicke superradiance is a universal phenomenon in ordered arrays. We present a theoretical framework -- which circumvents the exp…
Continuous Narrow-Linewidth Superradiance in Waveguide QED
University of Innsbruck（因斯布鲁克大学）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学和量子信息研究所）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Department of Physics, Harvard University（哈佛大学物理系）
Dicke Superradiance in Extended 2D Quantum Arrays Coupled to Metasurface Bound States in the Continuum
University of Manchester（曼彻斯特大学）；Newcastle University（纽卡斯尔大学）；A*STAR (Agency for Science, Technology and Research)（新加坡科技研究局）；Consejo Superior de Investigaciones Científicas（西班牙高等科学研究委员会）
Symbolic Quantum-Trajectory Method for Multichannel Dicke Superradiance
University of Innsbruck（因斯布鲁克大学）；Harvard University（哈佛大学）；TU Darmstadt（达姆施塔特工业大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
An outstanding challenge for color center-based quantum information processing technologies is the integration of optically-coherent emitters into scalable thin-film photonics. Here, we report on the integration of near-transform-limited silicon vacancy (V$_{\text{Si}}$) defects into microdisk resonators fabricated in a CMOS-compatible 4H-Silicon Carbide-on-Insulator platform. We demonstrate a single-emitter cooperativity of up to 0.8 as well as optical superradiance from a pair of color centers coupled to the same cavity mode. We investigate the effect of multimode interference on the photon …
We study quantitatively the breakdown of the rotating-wave approximation when calculating collective light emission by quantum emitters, in particular in the weak-excitation limit. Our starting point is a known multiple-scattering formalism where the full light-matter interaction leads to induced inter-emitter interactions described by the classical Green function of inhomogeneous dielectric media. When making the RWA in the light-matter interaction, however, these induced interactions differ from the classical Green function, and for free space we find a reduction of the interatomic interacti…
Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition wavelength are usually restricted to their early time behavior or to the few-excitation limit. We use herein a mean-field approach to reduce the complex many-body system to an effective two-atom master equation that includes all correlations up to second order and that can be numerically propagated in time. We find that three-dimensional and two-dimensional inver…
We study a system of two distant quantum emitters coupled via a one-dimensional waveguide where the electromagnetic field has a direction-dependent velocity. As a consequence, the onset of collective emission is non-simultaneous and, for appropriate parameters, while one of the emitters exhibits superradiance the other can be subradiant. Interference effects enable the system to radiate in a preferential direction depending on the atomic state and the field propagation phases. We characterize such directional emission as a function of various parameters, delineating the conditions for optimal …
Superradiance, characterized by the collective, coherent emission of light from an excited ensemble of emitters, generates photonic signals on timescales faster than the natural lifetime of an individual atom. The rapid exchange of coherence between atomic emitters and photonic fields in the superradiant regime enables a fast, broadband quantum memory. We demonstrate this superradiance memory mechanism in an ensemble of cold rubidium atoms and verify that this protocol is suitable for pulses on timescales shorter than the atoms' natural lifetime. Our simulations show that the superradiance mem…
Scaling theory of decoherence in Dicke superradiance
TU Darmstadt（达姆施塔特工业大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；CNRS and Université de Strasbourg（法国国家科学研究中心与斯特拉斯堡大学）
Dicke superrandiance is a cooperative phenomenon which arises from the collective coupling of an ensemble of atoms to the electromagnetic radiation. Here we discuss the quantifying of quantum coherence for the Dicke model of superradiance in the mean-field approximation. We found the single-atom $l_1$-norm of coherence is given by the square root of the normalized average intensity of radiation emitted by the superradiant system. This validates quantum coherence as a useful figure of merit towards the understanding of superradiance phenomenon in the mean-field approach. In particular, this res…
Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most sup…
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with non-vanishing dipole moment. We find that the two configurations produce similar far field i…
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ansätze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity…
Single-photon superradiance can emerge when a collection of identical emitters are spatially separated by distances much less than the wavelength of the light they emit, and is characterized by the formation of a superradiant state that spontaneously emits light with a rate that scales linearly with the number of emitters. This collective phenomena has only been demonstrated in a few nanomaterial systems, all requiring temperatures below 10K. Here, we rationally design a single colloidal nanomaterial that hosts multiple (nearly) identical emitters that are impervious to the fluctuations which …
