We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.
We have done simulating of factorization the number 15 on three qutrits, represented by the spins S = 1, by quantum annealing. We assume that strong one-spin interaction allow selectively operate on different transitions between levels of the each qutrit. We present a sequence of selective rotation operators to engineer from dipole-dipole interaction a time-dependent effective Hamiltonian necessary for solving the problem. Also we find dependence of fidelity versus different parameters: magnetic field, total annealing time, and duration of time step, when the continuous variation of the Hamilt…
We consider multiphoton dynamics of a quantum system composed of a three-state atom (a qutrit) and a single-mode photonic field in the ultrastrong and deep strong coupling regimes, when the coupling strength is comparable to or larger than the oscillator energy scale. We assume a qutrit to be in a polar-$Λ$ configuration in which two lower levels have mean dipole moments. Direct multiphoton resonant transitions revealing generalized Rabi oscillations, collapse, and revivals in atomic excitation probabilities for the ultrastrong couplings are studied. In the deep strong coupling regime particul…
If an atom is able to exhibit macroscopic dark periods, or electron shelving, then a driven system of two atoms has three types of fluorescence periods (dark, single and double intensity). We propose to use the average durations of these fluorescence types as a simple and easily accessible indicator of cooperative effects. As an example we study two dipole-interacting V systems by simulation techniques. We show that the durations of the two types of light periods exhibit marked separation-dependent oscillations and that they vary in phase with the real part of the dipole-dipole coupling consta…
The mutual dipole-dipole interaction of atoms in a trap can affect their fluorescence. Extremely large effects were reported for double jumps between different intensity periods in experiments with two and three Ba^+ ions for distances in the range of about ten wave lengths of the strong transition while no effects were observed for Hg^+ at 15 wave lengths. In this theoretical paper we study this question for configurations with three and four levels which model those of Hg^+ and Ba^+, respectively. For two systems in the Hg^+ configuration we find cooperative effects of up to 30% for distance…
We investigate the effect of the dipole-dipole interaction on the quantum jump statistics of three atoms. This is done for three-level systems in a V configuration and in what may be called a D configuration. The transition rates between the four different intensity periods are calculated in closed form. Cooperative effects are shown to increase by a factor of 2 compared to two of either three-level systems. This results in transition rates that are, for distances of about one wavelength of the strong transition, up to 100% higher than for independent systems. In addition the double and triple…
Resonant dipole-dipole interaction (RDDI) is ubiquitous in light-matter interacting systems and is responsible for many fascinating properties of collective radiations. Here we theoretically investigate the role of RDDI in electromagnetically induced transparency (EIT). The resonant dipole-dipole interactions manifest in the cooperative spontaneous emission of the probe light transition, which give rise a broadened linewidth and associated collective frequency shift. This cooperative linewidth originates from the nonlocal and long-range RDDI, which can be determined by the atomic density, opti…
We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency setup at high density. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local field induced phase modulation and show that it distinctively differs from the nonlinear self-phase modulation a strong pulse experiences in a Kerr medium.
We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the single resonant dipole case, and with a modified lifetime, due to the interactions between dipoles. Of particular interest is the kagome lattice, where the semiregular geometry permits simultaneous excitation of two dominant modes, one strongly subradiant, leading to an electromagnetically-induced-transparency-like interference in a two-level syst…
Cooperative effects in the fluorescence of two dipole-interacting atoms, with macroscopic quantum jumps (light and dark periods), are investigated. The transition rates between different intensity periods are calculated in closed form and are used to determine the rates of double jumps between periods of double intensity and dark periods, the mean duration of the three intensity periods and the mean rate of their occurrence. We predict, to our knowledge for the first time, cooperative effects for double jumps, for atomic distances from one and to ten wave lengths of the strong transition. The …
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the popula…
Dipole-dipole interaction between two two-level `atoms' in photonic crystal nanocavity is investigated based on finite-difference time domain algorithm. This method includes both real and virtual photon effects and can be applied for dipoles with different transition frequencies in both weak and strong coupling regimes. Numerical validations have been made for dipoles in vacuum and in an ideal planar microcavity. For dipoles located in photonic crystal nanocavity, it is found that the cooperative decay parameters and the dipole-dipole interaction potential strongly depend on the following four…
By coupling a probe transition to a Rydberg state using electro-magnetically induced transparency (EIT) we map the strong dipole-dipole interactions onto an optical field. We characterize the resulting cooperative optical non-linearity as a function of probe strength and density. We show that the effect of dipole blockade cannot be described using a mean-field but requires an $N$-atom cooperative model. Good quantitative agreement is obtained for three atoms per blockade with the $n=60$ Rydberg state. We place an upper-limit on the dephasing rate of the blockade spheres of $<110$ kHz.
In a closely packed ensemble of quantum emitters, cooperative effects are typically suppressed due to the dephasing induced by the dipole-dipole interactions. Here, we show that by adding sufficiently strong collective dephasing cooperative effects can be restored. In particular, we show that the dipole force on a closely packed ensemble of strongly driven two-level quantum emitters, which collectively dephase, is enhanced in comparison to the dipole force on an independent non-interacting ensemble. Our results are relevant to solid state systems with embedded quantum emitters such as colour c…
The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations, of which some evidence has been found in previous experiments. Here we present experimental results on the dynamics and the counting statistics of Rydberg excitations of ultra-cold Rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We compare our results with numeric…
We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $γ$ and $γ_0$ and a single parameter $Δ_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically f…
We show unusual cooperative two-photon resonance between two-modes of field inside a photonic crystal cavity. The two-photon resonance occurs when two off resonant quantum dots emit one photon in each cavity mode and de-excite simultaneously. In the presence of phonon coupling the conditions for two-photon resonance change significantly. Using such two-photon two-mode interaction we propose to generate entangled state of two qutrits. The basis of a qutrit are formed by the state of the cavity mode containing $0$, $1$ and $2$ photons. We also discuss effect of phonon coupling on negativity of t…
We demonstrate a cooperative optical non-linearity caused by dipolar interactions between Rydberg atoms in an ultra-cold atomic ensemble. By coupling a probe transition to the Rydberg state we map the strong dipole-dipole interactions between Rydberg pairs onto the optical field. We characterize the non-linearity as a function of electric field and density, and demonstrate the enhancement of the optical non-linearity due to cooperativity.
It has been theoretically demonstrated that two spins (qubits or qutrits), coupled by exchange interaction only, undergo a coupling-based joint Landau-Majorana-Stückelberg-Zener (LMSZ) transition when a linear ramp acts upon one of the two spins. Such a transition, under appropriate conditions on the parameters, drives the two-spin system toward a maximally entangled state. In this paper, effects on the quantum dynamics of the two qudits, stemming from the Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, are investigated qualitatively and quantitatively. The enriched Hamiltonia…
Abstract We investigate the spectral shift in collective forward scattering for a cold dense atomic cloud. The shift, sometimes called collective Lamb shift, results from resonant dipole-dipole interaction mediated by real and virtual photon exchange, forming many-body states displaying various super- and subradiant spectral behavior. The scattering spectrum reflects the overall radiative behavior from these states. However, it also averages out the radiative details associated with a single collective state, causing ambiguity in explaining the origin of the spectral shift and raising controve…
We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction combined with atom-field coupling can introduce additional interatomic correlations acting as a phase synchronizing factor. For the case of weakly interacting atoms with $J<\hbarω_0$, where $J$ is the interparticle coupling constant and $ω_0$ is the atomic frequency, dynamical regimes of cooperative relaxation of atoms are analyzed in Born-Markov approximation both numer…
On the basis of a quantum microscopic approach we study the cooperative effects induced by the dipole-dipole interaction in an ensemble of point-like impurity centers located near a charged perfectly conducting surface. We analyze the simultaneous influence of the modified spatial structure of field modes near the conductive surface and the electric field on the transition spectrum of an excited atom inside an ensemble and on the radiation trapping. We show that the electric field modifies the cooperative Lamb shift, as well as the character of sub- and superradiant decay. We also demonstrate …
We show that a cooperative atom response in an optical lattice to resonant incident light can be employed for precise control and manipulation of light on a subwavelength scale. Specific collective excitation modes of the system that result from strong light-mediated dipole-dipole interactions can be addressed by tailoring the spatial phase-profile of the incident light. We demonstrate how the collective response can be used to produce optical excitations at well-isolated sites on the lattice.
By utilizing strong optical resonant interactions in arrays of atoms with electric dipole transitions, we show how to synthesize collective optical responses that correspond to those formed by arrays of magnetic dipoles and other multipoles. Optically active magnetism with the strength comparable with that of electric dipole transitions is achieved in collective excitation eigenmodes of the array. By controlling the atomic level shifts, an array of spectrally overlapping, crossed electric and magnetic dipoles can be excited, providing a physical realization of a nearly-reflectionless quantum H…
We investigate cooperative fluorescence in a dilute cloud of strongly driven two-level emitters. Starting from the Heisenberg equations of motion, we compute the first-order scattering corrections to the saturation of the excited-state population and to the resonance-fluorescence spectrum, which both require going beyond the state-of-the-art linear-optics approach to describe collective phenomena. A dipole blockade is observed due to long range dipole-dipole coupling that vanishes at stronger driving fields. Furthermore, we compute the inelastic component of the light scattered by a cloud of m…
A simplified scheme for the investigation of cooperative effects in the quantum jump statistics of small numbers of fluorescing atoms and ions in a trap is presented. It allows the analytic treatment of three dipole-dipole interacting four-level systems which model the relevant level scheme of Ba+ ions. For the latter, a huge rate of double and triple jumps was reported in a former experiment and the huge rate was attributed to the dipole-dipole interaction. Our theoretical results show that the effect of the dipole-dipole interaction on these rates is at most 5% and that for the parameter val…
Plasmonic superradiance originates from the plasmon mediated strong correlation that builds up between dipolar emitters coupled to a metal nanoparticle. This leads to a fast burst of emission so that plasmonic superradiance constitutes ultrafast and extremely bright optical nanosources of strong interest for integrated quantum nano-optics platforms. We elucidate the superradiance effect by establishing the dynamics of the system, including all features like the orientation of the dipoles, their distance to the particle and the number of active plasmon modes. We determine an optimal configurati…
We study strong light-mediated resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a "super-atom", whose response is similar to electromagnetically-induced transparency, but which exhibits an ultra-narrow collective size-dependent subradiant resonance linewidth. The super-atom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions…
We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions, mediated by single-atom couplings to the shared electromagnetic vacuum, are shown to produce spatially-dependent cooperative Lamb shifts when spectroscopically interrogating the mHz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for state-of-the-art optical atomic clocks. Additionally, we demonstrate that excitation of the ato…
The influence of evanescent waves on the nature of optical cooperative effects in atomic ensembles in a waveguide
Peter the Great St. Petersburg Polytechnic University（圣彼得堡彼得大帝理工大学）；Institute for Analytical Instrumentation of RAS（俄罗斯科学院分析仪器研究所）；Ioffe Institute（约费研究所）
We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions in a three dimensional optical lattice. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate, and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We derive selection rules and a figure-of-merit for the dipole-dipole interaction matrix elements,…
In this paper, we study the competition between finite-size effects (i.e. discernibility of particles) and dipole-dipole interactions in few-atom systems coupled to the electromagnetic field in vacuum. We consider two hallmarks of cooperative effects, superradiance and subradiance, and compute for each the rate of energy radiated by the atoms and the coherence of the atomic state during the time evolution. We adopt a statistical approach in order to extract the typical behavior of the atomic dynamics and average over random atomic distributions in spherical containers with prescribed $k_0R$ wi…
Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to external light fields as they may host collective delocalized excitations (a form of excitons) with super- or subradiant character. Deeply subwavelength separations typically occur in molecular ensembles, where in addition to photon-electron interactions, electron-vibron couplings and vibrational relaxation processes play an important role. We provide analytical and numerical results on the modification of super- and subradiance in molecular rings of dipoles including excitations of the vibrational degrees of freedom.…
We present an experimental study of energy transfer in a thermal vapor of atomic rubidium. We measure the fluorescence spectrum in the visible and near infra-red as a function of atomic density using confocal microscopy. At low density we observe energy transfer consistent with the well-known energy pooling process. In contrast, above a critical density we observe a dramatic enhancement of the fluorescence from high-lying states that is not to be expected from kinetic theory. We show that the density threshold for excitation on the D1 and D2 resonance line corresponds to the value at which the…
We develop a quantum optical formalism to treat a two-dimensional array of atoms placed in an optical cavity. Importantly, and in contrast to typical treatments, we account for cooperative dipole-dipole effects mediated by the interaction of the atoms with the outside, non-cavity-confined modes. Based on the observation that scattering to these modes is largely inhibited due to these cooperative effects, we construct a generic formalism, independent of the specific cavity structure, and apply it to an array of non-saturated atoms. By further considering the atomic motion, we show that the inhi…
We report progress in the theory of photoluminescence and light scattering by two closely spaced particles. This study is based on our original method to derive the master equation for a system of coupled quantum emitters driven by a cw laser. We emphasise on the case when the emitters are two-level systems but notably different in their transition frequencies and transition moments. The master equation is shown to describe the dipole-dipole coupling and the cooperative entanglement between the particles naturally. It is provided by the use of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hi…
We have studied the interplay between disorder and cooperative scattering for single scattering limit in the presence of a driving laser. Analytical results have been derived and we have observed cooperative scattering effects in a variety of experiments, ranging from thermal atoms in an optical dipole trap, atoms released from a dark MOT and atoms in a BEC, consistent with our theoretical predictions.
The dynamics of two two-level dipole-dipole interacting atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity, is reported. Initially injecting only one excitation in the two atoms-cavity system, loss mechanisms asymptotically drive the matter sample toward a stationary maximally entangled state. The role played by the closeness of the two atoms with respect to such a cooperative behaviour is carefully discussed. Stationary radiation trapping effects are found and transparently interpreted.
Natural materials typically interact weakly with the magnetic component of light which greatly limits their applications. This has led to the development of artificial metamaterials and metasurfaces. However, natural atoms, where only electric dipole transitions are relevant at optical frequencies, can cooperatively respond to light to form collective excitations with strong magnetic, as well as electric, interactions, together with corresponding electric and magnetic mirror reflection properties. By combining the electric and magnetic collective degrees of freedom we show that ultrathin plana…
The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-S…
Whenever several quantum light emitters are brought in proximity with one another, their interaction with common electromagnetic fields couples them, giving rise to cooperative shifts in their resonance frequency. Such collective line shifts are central to modern atomic physics, being closely related to superradiance on one hand and the Lamb shift on the other. Although collective shifts have been theoretically predicted more than fifty years ago, the effect has not been observed yet in a controllable system of a few isolated emitters. Here, we report a direct spectroscopic observation of the …
Samples with few hundred atoms within a few micrometer sized region of space are large enough to provide efficient cooperative absorption and emission of light, and small enough to ensure strong dipole-dipole interactions when atoms are excited into high-lying Rydberg states. Based on a recently proposed collective encoding scheme, we propose to build few-qubit quantum registers in such samples. The registers can store and transmit quantum information in the form of single photons, and they can employ entanglement pumping protocols to perform ideally in networks for scalable quantum computing …
Implementation and representation of qudit multi-controlled unitaries and hypergraph states by N-body angular momentum couplings
Universidade Federal de Mato Grosso, Faculdade de Ciência e Tecnologia（马托格罗索联邦大学科学技术学院）；Centro Internacional de Física, Instituto de Física, Universidade de Brasília（巴西利亚大学物理研究所国际物理中心）
In this paper, we study cooperative scattering of low intensity light by a cloud of N two-level systems. We include the incident laser field driving these two-level systems and compute the radiation pressure force on the center of mass of the cloud. This signature is of particular interest for experiments with laser cooled atoms. Including the complex coupling between dipoles in a scalar model for dilute clouds of two-level systems, we obtain expression for cooperative scattering forces taking into account the collective Lamb shift. We also derive the expression of the radiation pressure force…
Light-matter interacting quantum systems manifest strong correlations that lead to distinct cooperative spontaneous emissions of subradiance or superradiance. To demonstrate the essence of long-range correlations in such systems, we consider an atomic array under the resonant dipole-dipole interactions (RDDI) and apply an interpretable machine learning with the integrated gradients to identify the crossover between the subradiant and superradiant sectors. The machine shows that the next nearest-neighbor couplings in RDDI play as much as the roles of nearest-neighbor ones in determining the who…
We investigate cooperative phenomena and superradiance for vibrational transitions in polar molecule spectroscopy when a high optical-depth (OD) sample is studied. Such cooperativity comes from the build-up of inter-particle coherence through dipole-dipole interactions and leads to the speed-up of decay process. We compare our calculation to recent work [Deiglmayr et al., Eur. Phys. J. D 65, 99 (2011)] and find very good agreement, suggesting that superradiant effects need to be included in a wide variety of ultracold molecule setups including vibrational and rotational states.
