We present analytical solutions for the evolution of collective states of N atoms. On the one hand is a (timed) Dicke state prepared by absorption of a single photon and exhibiting superradiant decay. This is in strong contrast to evolution of a symmetric Dicke state which is trapped for large atomic clouds. We show that virtual processes yield a small effect on the evolution of the rapidly decaying timed Dicke state. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important and provide new decay channels resulting in a slow decay of the otherwise trapped state.
We explore conditions for Dicke superradiance in a cloud of atoms by examining the Taylor series expansion of the photon emission rate at $t= 0$. By defining superradiance as an increasing photon emission rate for $t\sim 0$, we have calculated the conditions for superradiance for a variety of cases. We investigate superradiance as defined for photon emission into all angles as well as directional superradiance where the photon emission is only detected in a particular direction. Although all of the examples are for two level atoms that are fully inverted at $t=0$, we also give equations for pa…
Matter-wave superradiance is based on the interplay between ultracold atoms coherently organized in momentum space and a backscattered wave. Here, we show that this mechanism may be triggered by Mie scattering from the atomic cloud. We show how the laser light populates the modes of the cloud, and thus imprints a phase gradient on the excited atomic dipoles. The interference with the atoms in the ground state results in a grating, that in turn generates coherent emission, contributing to the backward light wave onset. The atomic recoil 'halos' created by the scattered light exhibit a strong an…
Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluores-cence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or "single-photon superradiance" , has been investigated much more recently, and superra-diant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute …
The interaction of light with an atomic sample containing a large number of particles gives rise to many collective (or cooperative) effects, such as multiple scattering, superradiance and subradiance, even if the atomic density is low and the incident optical intensity weak (linear optics regime). Tracing over the degrees of freedom of the light field, the system can be well described by an effective atomic Hamiltonian, which contains the light-mediated dipole-dipole interaction between atoms. This long-range interaction is at the origin of the various collective effects, or of collective exc…
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 ve…
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 …
This work examines superradiance in initially inverted clouds of \textit{multi-level} atoms. We develop a set of equations that can approximately calculate the temporal evolution of $N$ coupled atoms. This allows us to simulate clouds containing hundreds of multi-level atoms while eschewing the assumption and/or approximation of symmetric dipole-dipole interactions. This treatment is used to explore the effects that dephasing caused by elastic dipole-dipole interactions, and competition between multiple transitions have on superradiance. Both of these mechanisms place strong parametrical restr…
We theoretically characterize the collective radiative behaviour of N classical emitters near an interface between different dielectrics that supports the transfer of surface plasmon modes into the far-field of electromagnetic radiation. The phenomena of superradiance and surface plasmons can be combined to amplify the emitted radiation intensity S as S= A N^2 S_0 compared to a single emitter's intensity S_0 in free space. For a practical case study within the paper A=240, compared to A=1 in free space. We furthermore demonstrate that there are collective modes for which the intensity of the e…
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）
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…
We report observations of superradiance for atoms trapped in the near field of a photonic crystal waveguide (PCW). By fabricating the PCW with a band edge near the D$_1$ transition of atomic cesium, strong interaction is achieved between trapped atoms and guided-mode photons. Following short-pulse excitation, we record the decay of guided-mode emission and find a superradiant emission rate scaling as $\barΓ_{\rm SR}\propto\bar{N}\cdotΓ_{\rm 1D}$ for average atom number $0.19 \lesssim \bar{N} \lesssim 2.6$ atoms, where $Γ_{\rm 1D}/Γ_0 =1.1\pm0.1$ is the peak single-atom radiative decay rate int…
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…
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…
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…
The interplay between static and dynamic disorder and collective optical response in molecular ensembles is an important characteristic of nanoplasmonic and nanophotonic molecular systems. Here we investigate the cooperative superradiant response of a molecular ensemble of quantum emitters under the influence of environmental disorder, including inhomogeneous broadening (as induced by static random distribution of the molecular transition frequencies) and motional narrowing (as induced by stochastic modulation of these excitation energies). The effect of inhomogeneous broadening is to destroy …
We demonstrate a plasmonic route to control the collective spontaneous emission of two-level quantum emitters. Superradiance and subradiance effects are observed over distances comparable to the operating wavelength inside plasmonic nanochannels. These plasmonic waveguides can provide an effective epsilon-near-zero operation in their cut-off frequency and Fabry-Perot resonances at higher frequencies. The related plasmonic resonant modes are found to efficiently enhance the constructive (superradiance) or destructive (subradiance) interference between different quantum emitters located inside t…
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…
The interaction of an ensemble of atoms with common vacuum modes may lead to an enhanced emission into these modes. This phenomenon, known as superradiance, highlights the coherent nature of spontaneous emission, resulting in macroscopic entangled states in mundane situations. The complexity of the typical observations of superradiance, however, masks its quantum nature, allowing alternative classical interpretations. Here we stress how this picture changed with the implementation ten years ago of a new process for single-photon generation from atomic ensembles. We present then the last piece …
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）
Light emitters in a single-mode nanolaser interact with the same cavity field, that gives rise to polarization correlations which transform the cavity mode. Usually these correlations are ignored, however, collective phenomena can lead to the distinct sub- and superradiance, whose fully quantum description is challenging. Here, we develop a simple yet rigorous picture of radiative transitions in single-mode nanolasers that accounts for polarization correlations. We show that the collective behavior of emitters modifies the photonic density of states leading to gain-dependent Purcell enhancemen…
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 present quantum-mechanical approach for collective spontaneous emission (superradiance) of emitters (as atoms) near metal nanoparticle, when frequencies of transitions of emitters coincide with frequency of localized plasmon resonance of the nanoparticle. Our approach is based on Schrodinger description and it uses wave functions of states of systems. Interactions between emitters and between the nanoparticle and emitters are taken into account. We consider an example of two emitters and show that radiation is occurred through symmetric states of emitters as it is in Dicke model of superrad…
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…
We present an optical picture of linear-optics superradiance, based on a single scattering event embedded in a dispersive effective medium composed by the other atoms. This linear-dispersion theory is valid at low density and in the single-scattering regime, i.e., when the exciting field is largely detuned. The comparison with the coupled-dipole model shows a perfect agreement for the superradiant decay rate. Then we use two advantages of this approach. First we make a direct comparison with experimental data, without any free parameter, and show a good quantitative agreement. Second, we addre…
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 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…
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…
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…
A simplified theory for the wavepackets of the photons emitted during the read process of a quantum memory formed by cold atoms is provided. We arrive at analytical expressions for the single- and double-photon emissions, evidencing superradiant features in both cases. In the two-photon case, both photons are emitted in the same spatiotemporal mode, characterizing a superradiant emission of a Fock state of light with two excitations. Experiments confirm the theoretical predictions with a satisfactory agreement.
We use quantum-electrodynamical approach to study the initial stage of Dicke superradiance from a system of two-level atoms. Applying the zeroth-order Magnus approximation, we obtain the expression for the mean number of quanta emitted in the presence of thermal fluctuations of the electromagnetic field.
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…
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）
