Cooperative Spontaneous Emission Research Articles

Resonant dipole-dipole interactions in electromagnetically induced transparency

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, optical depth, and macroscopic length scales of the atomic ensemble. We present that EIT spectroscopy essentially demonstrates all-order multiple scattering of RDDI. Furthermore, we find that EIT transparency window becomes narrower as the cooperative linewidth increases, which essentially reduces the storage efficiency of slow light as EIT-based quantum memory application.

Generating long-lived entangled states with free-space collective spontaneous emission

Considering the paradigmatic case of a cloud of two-level atoms interacting through common vacuum modes, we show how cooperative spontaneous emission, which is at the origin of superradiance, leads the system to long-lived entangled states at late times. These subradiant modes are characterized by an entanglement between all particles, independently of their geometrical configuration. While there is no threshold on the interaction strength necessary to entangle all particles, stronger interactions lead to longer-lived entanglement.

Correlations in superradiance of a two-dimensional system

The process of cooperative spontaneous emission in a system of two-level emitters interacting via electromagnetic field is analyzed using the Bogolyubov reduced description method, which provides the possibility of studying the state of the generated field. Field macrostates are described with electric and magnetic field amplitudes and binary correlation functions of their components. Since the previously obtained set of differential equations describing the Dicke system evolution with considering field correlations is very cumbersome, we must find some way of simplifying the model to make it accessible for numerical modeling. The general picture of correlation development can be elucidated with using one- and two-dimensional models. The paper presents the set of evolution equations for Dicke system with fixed orientation of dipole moments of emitters forming a two-dimensional structure. The material equations and equilibrium correlations are discussed. The transition to the Cauchy problem for ordinary differential equations is proposed.

Collective spontaneous emission of two entangled atoms near an oscillating mirror

We consider the cooperative spontaneous emission of a system of two identical atoms interacting with the electromagnetic field in the vacuum state and in the presence of an oscillating mirror. We assume that the two atoms, one in the ground state and the other in the excited state, are prepared in a correlated (symmetric or antisymmetric) Bell-type state. We also suppose that the perfectly reflecting plate oscillates adiabatically, with the field modes satisfying the boundary conditions at the mirror surface at any given instant, so that the time dependence of the interaction Hamiltonian is entirely enclosed in the instantaneous atom-wall distance. Using time-dependent perturbation theory, we investigate the spectrum of the radiation emitted by the two-atom system, showing how the oscillation of the boundary modifies the features of the emitted spectrum, which exhibits two lateral peaks not present in the case of a static boundary. We also evaluate the transition rate to the collective ground state of the two-atom system in both cases of the superradiant (symmetric) and subradiant (antisymmetric) state. We show that it is modulated in time and that the presence of the oscillating mirror can enhance or inhibit the decay rate compared to the case of atoms in vacuum space or near a static boundary. Our results thus suggest that a dynamical (i.e., time-modulated) environment can offer further possibilities to control and manipulate radiative processes of atoms or molecules nearby, such as the cooperative decay, and strongly indicate a similar possibility for other radiative processes, for example, the resonance interaction and the energy transfer between atoms or molecules.

Universal trapping law induced by an atomic cloud in single-photon cooperative dynamics

Single-photon cooperative dynamics of an assembly of two-level quantum emitters coupled by a bosonic bath are investigated. The bosonic bath is general and it can be anything as long as the exchange of excitations between quantum emitters and bath is present. In these systems, it is found that the population on the excited emitter keeps a simple and universal trapping law due to the existence of system's dark states. Different from the trapping regime caused by photonemitter dressed states, this type of trapping is only associated with the number of quantum emitters. According to the trapping law, the cooperative spontaneous emission at single-photon level in this kind of systems is universally inhibited when the emitter number is large enough.

Cooperative spontaneous emission via a renormalization approach: Classical versus semiclassical effects

We address the many-atom emission of a dilute cloud of two-level atoms through a renormalized perturbation theory. An analytical solution for the truncated coupled-dipole equations is derived, which contains an effective spectrum associated to the initial conditions. Our solution is able to distinguish precisely classical from semi-classical predictions for large atomic ensembles. This manifests as a reduction of the cooperativity in the radiated power for higher atomic excitation, in disagreement with the fully classical prediction from linear optics. Moreover, the second-order cooperative emission appears accurate over several single atom lifetimes and for interacting regimes stronger than those permitted in conventional perturbation theory. We can compute the semiclassical dynamics of hundred thousand of interacting atoms with ordinary computational resources, which makes our formalism particularly promising to probe the nonlinear dynamics of quantum many-body systems that emerge from cumulant expansions.

THz Superradiance from a GaAs: ErAs Quantum Dot Array at Room Temperature

We report that an ErAs quantum-dot array in a GaAs matrix under 1550 nm pulsed excitation produces cooperative spontaneous emission—Dicke superradiance—in the terahertz frequency region at room temperature. Two key points pertain to the experimental evidence: (i) the pulsed THz emission power is much greater than the continuous wave (CW) photomixing power; and (ii) the ultrafast time-domain waveform displays ringing cycles. A record of ~117 μW pulsed THz power was obtained, with a 1550 nm-to-THz power conversion efficiency of ~0.2%.

Enhanced superradiance of quantum sources near nanoscaled media

We develop a rigorous theory for nanophotonic cooperative spontaneous emission of an ensemble of quantum emitters near matter, which also incorporates absorption. Such theory is highly requested since one should expect that in the field of nanophotonics the close-by emitters will emit cooperatively simultaneously with strong interaction with the exotic metamaterial complex dielectric function. The closed-form model developed here considers the buildup both of interemitter correlation over time through emitter transitions via the mutual field and of geometry-induced spatial correlation. The presence of matter alters the local density of states (LDOS), resulting in modified decay rate and emission intensity for the entire ensemble relative to values of spontaneous emission in free space. The superradiant total emission is separable into a quantum-mechanical time-dependent part and a classical space-dependent part, both being functions of the LDOS. Two distinct radiative emitter--far-field coupling mechanisms, which together account for the superradiant emission, are obtained---the coupling of every individual emitter with the far field and the coupling of emitter pairs to the far field. The calculations for superradiating emitters near silver and near-zero epsilon (NZE) materials were performed with the following results: the silver sphere augments the superradiant far-field intensity and rate by up to 400 and 1000%, respectively, while the NZE sphere enhances the far-field intensity and rate of the superradiance by approximately 1400 and 400%, respectively.

Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

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 $\gamma$ and $\gamma_0$ and a single parameter $\Delta_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically for up to 30 atoms, and obtain the large-$N$-limit by amean-field approach. We find that there is a critical difference $\gamma_0-\gamma$ that depends on $N$ beyond which superradiance is lost. We show that exact non-trivial dark states (i.e. states other than the ground state with vanishing spontaneous emission) only exist for $\gamma=\gamma_0$, and that those states (dark when $\gamma=\gamma_0$) are subradiant when $\gamma<\gamma_0$.

Cooperative spontaneous emission of nano-emitters with inter-emitter coupling in a leaky microcavity

We study the spontaneous emission from a few two-level nano-emitters placed in a leaky microcavity with Lorentzian spectral density near a critically damped regime. Collective features of the spontaneous emission are investigated by numerical analysis of the excitation dynamics when initially one nano-emitter is totally excited but we do not know which one. The results show that there are three decay rates in the excitation dynamics, two for simple exponential decays and one for damped oscillatory decay. The excitation dynamics is found to critically depend on the regime of the system. It is shown that the spontaneous emission is enhanced or suppressed depending on whether the system is in the underdamped or overdamped regime, respectively. On the other hand, the cooperative spontaneous emission is suppressed in the underdamped while it is enhanced in the overdamped regime. Furthermore, the effect of the direct inter-emitter coupling on the breaking of the cooperativeness of the spontaneous emission is shown as well.

Coherent control of cooperative spontaneous emission from two identical three-level atoms in a photonic crystal

The coherent control of cooperative spontaneous emission from two identical non-overlapping three-level atoms in the V-configuration located within a photonic band gap (PBG) material with two resonant frequencies near the upper band edge of the PBG and confined to a region small in comparison to their radiation wavelengths but still greater than their atomic sizes is investigated. The dependencies of cooperative effects in which a photon emitted by one atom is reabsorbed by the other atom on the inter-atomic separation, on the initial state of the two-atom system, on the strength of the driving control laser field, and on the detuning of the atomic resonant frequencies from the upper band edge frequency is analyzed so as to identify the conditions for which these cooperative effects are enhanced or inhibited. Cooperative effects between atoms are shown to be influenced more by the PBG than by the nature of the atomic transitions involved. Excited state populations as well as coherences between excited levels are expressed in terms of time-dependent amplitudes which are shown to satisfy coupled integro-differential equations for which analytic solutions are derived under special conditions. Unlike for the case of one atom in a PBG where the fractional non-zero steady state populations on the excited levels as well as the coherence between the excited levels are constants independent of time, in the case of two atoms in PBG these quantities continuously oscillate as a manifestation of beating due to the continuous exchange between the two atoms of the photon trapped by the PBG. The values of these quantities as well as the amplitudes and frequencies of their oscillations depend of the parameters of the system, providing different ways of manipulating the system. The general formalism presented here is shown to recapture the special results of investigations of similar systems in free space when the non-Markovian memory kernels of the PBG are replaced by delta function dependent Markovian memory kernels.

Effect of atomic distribution on cooperative spontaneous emission

We study cooperative single-photon spontaneous emission from N multilevel atoms for different atomic distributions in optical vector theory. Instead of the average approximation for interatomic distance or the continuum approximation (sums over atoms replaced by integrals) for atomic distribution, the positions of every atom are taken into account by numerical calculation. It is shown that the regularity of atomic distribution has considerable influence on cooperative spontaneous emission. For a small atomic sample (compared with radiation wavelength), to obtain strong superradiance not only needs the uniform excitation (the Dicke state) but also requires the uniform atomic distribution. For a large sample, the uniform atomic distribution is beneficial to subradiance of the Dicke state, while the influence of atomic distribution on the timed Dicke state is weak and its time evolution obeys exponential decay approximately. In addition, we also investigate the corresponding emission spectrum and verify the directed emission for the timed Dicke state for a large atomic sample.

Cooperative spontaneous emission of three identical atoms

We study cooperative single-photon spontaneous emission from three multilevel atoms with one of them being excited for different atomic configurations in optical vector theory. The dynamic evolution is solved by finding the eigenvalues of a 3 \ifmmode\times\else\texttimes\fi{} 3 matrix, and then the relevant decay rates and Lamb shifts are obtained analytically. It is shown that the symmetry of atomic configuration has a big influence on the super-radiance of the system. To obtain strong super-radiance requires not only the distances among the three atoms to be much shorter than the wavelength, but also to have symmetrical distribution. We also calculate the emission spectra and find that it normally has three peaks, but it has two peaks under the equilateral-triangle configuration.

Resonant dipole–dipole interaction in confined and strong-coupling dielectric geometries

Using the electromagnetic response function of an electric dipole located within a dielectric geometry, we derive the mathematical equivalence between the classical response and quantum mechanical resonant dipole–dipole interaction between two quantum objects (atoms, quantum dots, etc). Cooperative spontaneous emission likewise emerges from this equivalence. We introduce a practical numerical technique using finite difference time domain for calculating both dipole–dipole interaction and collective spontaneous emission in confined dielectric structures, where strong light–matter coupling might arise. This method is capable of obtaining resonant dipole–dipole interaction over a wide range of frequencies in a single run. Our method recaptures the results of quantum mechanical second order perturbation theory for weak light–matter coupling. In strong coupling situations such as near a photonic band edge, second order Rayleigh–Schrödinger perturbation theory leads to divergences, and instead Brillouin–Wigner perturbation theory is required. This is equivalent to the use of a variational wavefunction to describe the exciton transfer between initial and final states. We introduce a system of coupled classical oscillators, that describes resonant dipole–dipole interaction and vacuum Rabi splitting in the strong-coupling regime, and that provides an effective numerical scheme based on the finite difference time domain method. This includes the effects of quantum entanglement and the correlation of quantum fluctuations. We discuss the crossover to Forster energy transfer when quantum correlations between the dipoles are damped by strong environmental interactions.

Manipulating the Annihilation Dynamics of Positronium via Collective Radiation

A method is investigated to manipulate the annihilation dynamics of a dense gas of positronium atoms employing superradiance and subradiance regimes of the cooperative spontaneous emission of the system. The corresponding annihilation dynamics is explored in two setups with regard to its fundamental novel properties and controlled by the gas density and by the intensity of a driving strong resonant laser field. In particular, the method allows us to increase the annihilation lifetime of an ensemble of positronium atoms by trapping the atoms in the excited state via collective radiative effects in the resonant laser field. In the second setup, the effect is enhanced by employing a cavity field. The maximum lifetime increase is by a factor of about 200 for para-positronium and by a factor of about 100 for ortho-positronium.

Superradiance from one-dimensionally aligned ZnO nanorod multiple-quantum-well structures

Using one-dimensionally aligned ZnO nanorod multiple-quantum-well structures (MQWs), we observed a superradiance, i.e., a cooperative spontaneous emission. We confirmed that the excitation power dependence of the emissions from the MQWs originated from the coherent coupling of the QWs due to the well organization at nanoscale. We identified two QWs with cooperative emission. Additionally, we evaluated the number of coherently coupled QWs sets of four that resulted in the superradiance. Our findings provide criteria for designing nanoscale synergetic devices without the use of an external cavity.

Collective spontaneous emission beyond the rotating-wave approximation

The collective spontaneous emission of N multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The counter-rotating terms are included using a unitary transformation method. We analyze the decay dynamics starting from two initial conditions, the standard Dicke and timed Dicke states. In addition to the dependence on ensemble volume and density, we also study the effect of the ensemble geometry on cooperative emission for spheres, cubes, and quasi-two-dimensional shapes in different orientations. Finally, time-dependent cooperative spontaneous emission rates are introduced and investigated.

Giant superfluorescent bursts from a semiconductor magneto-plasma

Currently, considerable resurgent interest exists in the concept of superradiance (SR), i.e., accelerated relaxation of excited dipoles due to cooperative spontaneous emission, first proposed by Dicke in 1954. Recent authors have discussed SR in diverse contexts, including cavity quantum electrodynamics, quantum phase transitions, and plasmonics. At the heart of these various experiments lies the coherent coupling of constituent particles to each other via their radiation field that cooperatively governs the dynamics of the whole system. In the most exciting form of SR, called superfluorescence (SF), macroscopic coherence spontaneously builds up out of an initially incoherent ensemble of excited dipoles and then decays abruptly. Here, we demonstrate the emergence of this photon-mediated, cooperative, many-body state in a very unlikely system: an ultradense electron-hole plasma in a semiconductor. We observe intense, delayed pulses, or bursts, of coherent radiation from highly photo-excited semiconductor quantum wells with a concomitant sudden decrease in population from total inversion to zero. Unlike previously reported SF in atomic and molecular systems that occur on nanosecond time scales, these intense SF bursts have picosecond pulse-widths and are delayed in time by tens of picoseconds with respect to the excitation pulse. They appear only at sufficiently high excitation powers and magnetic fields and sufficiently low temperatures - where various interactions causing decoherence are suppressed. We present theoretical simulations based on the relaxation and recombination dynamics of ultrahigh-density electron-hole pairs in a quantizing magnetic field, which successfully capture the salient features of the experimental observations.

Cooperative Spontaneous Emission from Nanocrystals to a Surface Plasmon Polariton in a Metallic Nanowire

We analyze the cooperative spontaneous emission of optically excited nanocrystals into surface plasmon polaritons propagating on the surface of a cylindrical metallic nanowire. The spontaneous emission probability of the nanocrystals is obtained by perturbative expansions with and without dipole-dipole interaction among nanocrystals in order to see the cooperative effects. The spontaneous emission probability depends on the radial and axial distributions, as well as on the dipolar orientation of nanocrystals. It is shown that the spontaneous emission probability is strongly influenced by dipole-dipole interaction, axial distribution, and dipolar orientation of nanocrystals for closely spaced nanocrystals.

Cooperative spontaneous emission in nonuniform media

The subject of this paper is modification of cooperative spontaneous emission by a nonuniform medium, with nonuniform distributions of electromagnetic field. A brief analyzis is presented and it is postulated, that if spontaneous emission from an atom is strongly suppressed, cooperative emission with another atom may be a preferred emission channel and counteract the suppression.