A collective description of density matrix is presented for identical multi-level atoms, which are either excited initially, driven coherently or pumped incoherently. The density matrix is defined as expectation value of projection or transition operators in a basis of atom's product states. The identical matrix elements are identified with several integers, which specify uniquely the involved operators. To remove the redundancy, these identical elements are treated as single quantity and the equation for this quantity is dervied by mapping the transition or projection operators to a single vector specified with these integers. As a result, the number of computed elements increases polynomially rather than exponentially with the number of atoms. As an example, we carry out exact simulation of hundreds of two-level atoms and demonstrate the different conditions for observing superradiance and superfluorescence.
Superradiance in an ensemble of atoms leads to the collective enhancement of radiation in a particular mode shared by the atoms in their spontaneous decay from an excited state. The quantum aspects of this phenomenon are highlighted when such collective enhancement is observed in the emission of a single quantum of light. Here we report a further step in exploring experimentally the nonclassical features of superradiance by implementing the process not only with single excitations, but also in a two-excitations state. Particularly we measure and theoretically model the wave-packets correspondi…
Recently, it has been suggested that the collective radiative decay of two point-like quantum emitters coupled to a waveguide, separated by a distance comparable to the coherence length of a spontaneously emitted photon, leads to an apparent $^{\prime}$superradiance paradox$^{\prime}$ by which one cannot decide whether independent or collective emission occurs. The resolution of the paradox stems from the strong non-Markovian dynamics arising from the delayed field-mediated atom interaction. Here we suggest an integrated optics platform to emulate the superradiance paradox, based on photon esc…
We develop a formalism for modelling exact time dynamics in waveguide quantum electrodynamics (QED) using the real-space approach. The formalism does not assume any specific configuration of emitters and allows the study of Markovian dynamics fully analytically and non-Markovian dynamics semi-analytically with a simple numerical integration step. We use the formalism to study subradiance, superradiance and bound states in continuum. We discuss new phenomena such as subdivision of collective decay rates into symmetric and anti-symmetric subsets and non-Markovian superradiance effects that can l…
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）
Absence of Entanglement Growth in Dicke Superradiance
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（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；TU Darmstadt, Institute for Applied Physics（达姆施塔特工业大学应用物理研究所）
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…
In an ensemble of identical atoms, cooperative effects like sub- or superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multi-level systems are more difficult to handle. In this work we show that in a system of atoms or nuclei under the action of an external magnetic field, the collective contribution to the level shifts can amount to seizable deviations from the single-atom Zeeman or magnetic hyp…
An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from $300\,$K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance …
Collective effects in the interaction of light with ensembles of identical scatterers play an important role in many fields of physics. However, often the term ``identical'' is not accurate due to the presence of hyperfine fields which induce inhomogeneous transition shifts and splittings. Here we develop a formalism based on the Green function method to model the linear response of such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact formula for the collective spectrum, which exhibits deviations from the uniform frequency shift and broadening expected of two level s…
Quantum effects, prevalent in the microscopic scale, generally elusive in macroscopic systems due to dissipation and decoherence. Quantum phenomena in large systems emerge only when particles are strongly correlated as in superconductors and superfluids. Cooperative interaction of correlated atoms with electromagnetic fields leads to superradiance, the enhanced quantum radiation phenomenon, exhibiting novel physics such as quantum Dicke phase and ultranarrow linewidth for optical clocks. Recent researches to imprint atomic correlation directly demonstrated controllable collective atom-field in…
We study non-Markovian enhancement effects in the spontaneous emission of a collective excitation in a linear chain of up to 100 qubits coupled to a 1D waveguide. We find that for a critical separation of qubits, the system exhibits super-superradiant (SSR) behavior leading to collective decay stronger than the usual Dicke superradiance. Here, time-delayed coherent quantum feedback effects are at play on top of the usual Dicke superradiance effects. We find a linear scaling for the SSR decay rate with increasing qubit number $N$ such that $Γ_{\rm SSR} \sim 2.277 N γ_0$, where $γ_0$ is the sing…
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…
Intriguing collective spontaneous cascade emissions have recently been realized. In despite of much success, a depth understanding of the complexity is still lacking. With this motivation, a new simple cascade superradiance model is developed in this work. The existing model of identical two-level atoms is reexamined with a new insight. Temporal evolutions of average time delays and the fluctuations are introduced and the superradiance time delays are obtained in four different ways. These formulations allow to extend the two-level model to a cascade three-level model. The correlated two-mode …
We report a time-resolved study of collective emission in dense ensembles of two-level atoms. We compare, on the same sample, the build-up of superradiance and subradiance from the ensemble when driven by a strong laser. This allows us to measure the dynamics of the population of superradiant and subradiant states as a function of time. In particular we demonstrate the build up in time of subradiant states through the superradiant dynamics. This illustrates the dynamics of the many-body density matrix of superradiant ensembles of two-level atoms when departing from the ideal conditions of Dick…
Robust Superradiance and Spontaneous Spin Ordering in Disordered Waveguide Quantum Electrodynamics
Technical University of Munich（慕尼黑工业大学）；TUM School of Natural Sciences, Physics Department（慕尼黑工业大学自然科学学院物理系）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
From superradiance to collective EIT in three-level ensembles
Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；Instituto de Ciências e Engenharia, Universidade Estadual Paulista - Câmpus de Itapeva（科学与工程学院，圣保罗州立大学-伊塔佩瓦校区）；Instituto de Física, Universidade Federal de Goiás（物理研究所，戈亚斯联邦大学）
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）
Dicke superradiance in degenerate quantum matter: interplay of exchange statistics and spatial confinement
Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；TU Darmstadt（达姆施塔特工业大学）
The condition of phase matching prohibits the transfer of excitation from free-space photons to surface plasmon polaritons (SPP). We propose and analyze a scheme that excites an ensemble of emitters in a collective state, which is phase matched with the SPP by the optical pulses used for its preparation. By a collective enhancement the ensemble, hence, emits an SPP in a well defined direction. We demonstrate the scheme by analyzing the launching of near-infrared graphene SPP. Our theory incorporates the dispersive and dissipative properties of the plasmon modes to evaluate the non-Markovian em…
Flat bands play an important role in diffraction-free photonics and attract fundamental interest in many-body physics. Here we report the engineering of flat-band localization of collective excited states of atoms in Creutz superradiance lattices with tunable synthetic gauge fields. Magnitudes and phases of the lattice hopping coefficients can be independently tuned to control the state components of the flat band and the Aharonov-Bohm phases. We can selectively excite the flat band and control the flat-band localization with the synthetic gauge field. Our study provides a room-temperature pla…
Fully inverted atoms placed at exactly the same location synchronize as they deexcite, and light is emitted in a burst (known as "Dicke's superradiance"). We investigate the role of finite interatomic separation on correlated decay in mesoscopic chains, and provide an understanding in terms of collective jump operators. We show that the superradiant burst survives at small distances, despite Hamiltonian dipole-dipole interactions. However, for larger separations, competition between different jump operators leads to dephasing, suppressing superradiance. Collective effects are still significant…
Super- and subradiance are usually described in the framework of Dicke collective states, which is an ``atomic picture'' in which the electromagnetic field only provides an effective interaction between the atoms. Here, we discuss a complementary picture, in which we describe the propagation and scattering of light in the atomic medium, which provides a complex susceptibility and scatterers. This ``optical picture'' is valid in the linear-optics regime for disordered samples and is mainly relevant at low density, when the susceptibility and scattering cross-section can be computed from simple …
We investigate laser-induced quantum interference phenomena in superradiance processes and in an ensemble of initially excited $Λ-$type closely packed three-level emitters. The lower doublet levels are pumped with a coherent laser field. Due to constructive quantum interference effects, the superradiance occurs on a much weaker atomic transition which is not the case in the absence of the coherent driving. This result may be of visible relevance for enhancing ultraweak transitions in atomic or atomic-like systems, respectively, or for high-frequency lasing effects.
Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light wave. It is shown that at a certain critical number of atoms in the ensemble the stabilization effect of the excited state of the ensemble relative to collective atomic decay is possible, with superradiance of the atomic ensemble being suppressed. When the number of atoms is close to the critical value, superradiance exhibits features that are opposite to the e…
Emission and absorption of light lie at the heart of light-matter interaction. Although emission and absorption rates are regarded as intrinsic properties of atoms and molecules, various ways to modify these rates have been sought in applications such as quantum information processing, metrology and light-energy harvesting. One promising approach is to utilize collective behaviour of emitters in the same way as in superradiance5. Although superradiance has been observed in diverse systems, its conceptual counterpart in absorption has never been realized11 until now. Here we demonstrate enhance…
We report direct, time-resolved observations of single-photon superradiance in a highly extended, elliptical sample of cold 87Rb atoms. The observed rapid decay rate is accompanied by its counterpart, the cooperative Lamb shift. The rate of the strongly directional decay, and the associated shift, scale linearly with the number of atoms and show a strong dependence on the sample shape, demonstrating the collective nature of the observed quantities.
In super- or subradiance, a quantum superposition of excited atoms collectively emits a photon much more or much less rapidly than an isolated atom. Superradiant and subradiant lifetimes have been derived for finite spheres of uniform media, either by simulating random samples or by expanding in spherical harmonics and analyzing Bessel functions. We introduce a simple regulator that applies to unbounded media, enabling trivial derivation and analysis of lifetimes via elementary Fourier techniques. The regulator can be interpreted as a correlation length for atomic positions; the regularized sy…
Floquet modulation has been widely used in optical lattices for coherent control of quantum gases, in particular for synthesizing artificial gauge fields and simulating topological matters. However, such modulation induces heating which can overwhelm the signal of quantum dynamics in ultracold atoms. Here we report that the thermal motion, instead of being a noise source, provides a new control knob in Floquet-modulated superradiance lattices, which are momentum-space tight-binding lattices of collectively excited states of atoms. The Doppler shifts combined with Floquet modulation provide eff…
We present a proposal for a probing scheme utilizing Dicke superradiance to obtain information about ultracold atoms in optical lattices. A probe photon is absorbed collectively by an ensemble of lattice atoms generating a Dicke state. The lattice dynamics (e.g., tunneling) affects the coherence properties of that Dicke state and thus alters the superradiant emission characteristics -- which in turn provides insight into the lattice (dynamics). Comparing the Bose-Hubbard and the Fermi-Hubbard model, we find similar superradiance in the strongly interacting Mott insulator regime, but crucial di…
Effects of retardation on many-body superradiance in chiral waveguide QED
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
We study the collective decay rates of multi-dimensional quantum networks in which one-dimensional waveguides form an intersecting hyper-rectangular lattice, with qubits located at the lattice points. We introduce and motivate the \emph{dimensional reduction of poles} (DRoP) conjecture, which identifies all collective decay rates of such networks via a connection to waveguides with a one-dimensional topology (e.g. a linear chain of qubits). Using DRoP, we consider many-body effects such as superradiance, subradiance, and bound-states in continuum in multi-dimensional quantum networks. We find …
Disorder-Induced Enhancement of Fermionic Superradiance
CNR-INO（意大利国家研究委员会光学研究所）；University of Trento（特伦托大学）；INFN-TIFPA（意大利国家核物理研究所-特伦托基础物理与应用研究所）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）
