Many-Body Subradiant Excitations in Metamaterial Arrays: Experiment and Theory

Negative refraction of light in an atomic medium

The quest to manipulate light propagation in ways not possible with natural media has driven the development of artificially structured metamaterials. One of the most striking effects is negative refraction, where the light beam deflects away from the boundary normal. However, due to material characteristics, the applications of this phenomenon, such as lensing that surpasses the diffraction limit, have been constrained. Here, we demonstrate negative refraction of light in an atomic medium without the use of artificial metamaterials, employing essentially exact simulations of light propagation. High transmission negative refraction is achieved in atomic arrays for different level structures and lattice constants, within the scope of currently realised experimental systems. We introduce an intuitive description of negative refraction based on collective excitation bands, whose transverse group velocities are antiparallel to the excitation quasi-momenta. We also illustrate how this phenomenon is robust to lattice imperfections and can be significantly enhanced through subradiance.

Nonlocal metasurface for dark-field edge emission

Nonlocal effects originating from interactions between neighboring meta-atoms introduce additional degrees of freedom for peculiar characteristics of metadevices, such as enhancement, selectivity, and spatial modulation. However, they are generally difficult to manipulate because of the collective responses of multiple meta-atoms. Here, we experimentally demonstrate the nonlocal metasurface to realize the spatial modulation of dark-field emission. Plasmonic asymmetric split rings (ASRs) are designed to simultaneously excite local dipole resonance and nonlocal quasi-bound states in the continuum and spatially extended modes. With one type of unit, nonlocal effects are tailored by varying array periods. ASRs at the metasurface's edge lack sufficient interactions, resulting in stronger dark-field scattering and thus edge emission properties of the metasurface. Pixel-level spatial control is demonstrated by simply erasing some units, providing more flexibility than conventional local metasurfaces. This work paves the way for manipulating nonlocal effects and facilitates applications in optical trapping and sorting at the nanoscale.

Meta-Atoms with Toroidal Topology for Strongly Resonant Responses

A conductive meta-atom of toroidal topology is studied both theoretically and experimentally, demonstrating a sharp and highly controllable resonant response. Simulations are performed both for a free-space periodic metasurface and a pair of meta-atoms inserted within a rectangular metallic waveguide. A quasi-dark state with controllable radiative coupling is supported, allowing to tune the linewidth (quality factor) and lineshape of the supported resonance via the appropriate geometric parameters. By conducting a rigorous multipole analysis, we find that despite the strong toroidal dipole moment, it is the residual electric dipole moment that dictates the electromagnetic response. Subsequently, the structure is fabricated with 3D printing and coated with silver paste. Importantly, the structure is planar, consists of a single metallization layer and does not require a substrate when neighboring meta-atoms are touching, resulting in a practical, thin and potentially low-loss system. Measurements are performed in the 5 GHz regime with a vector network analyzer and a good agreement with simulations is demonstrated.

Linear optical elements based on cooperative subwavelength emitter arrays

We describe applications of two-dimensional subwavelength quantum emitter arrays as efficient optical elements in the linear regime. For normally incident light, the cooperative optical response, stemming from emitter-emitter dipole exchanges, allows the control of the array's transmission, its resonance frequency, and bandwidth. Operations on fully polarized incident light, such as generic linear and circular polarizers as well as phase retarders can be engineered and described in terms of Jones matrices. Our analytical approach and accompanying numerical simulations identify optimal regimes for such operations and reveal the importance of adjusting the array geometry and of the careful tuning of the external magnetic fields amplitude and direction.

Control of Localized Single- and Many-Body Dark States in Waveguide QED

Subradiant states in a finite chain of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and their controlled release. As one can maximally store one energy quantum per emitter, storing multiple excitations requires delocalized states, which typically exhibit fermionic correlations and antisymmetric wave functions, thus making them hard to access experimentally. Here we identify a new class of quasilocalized dark states with up to half of the qubits excited, which only appear for lattice constants of an integer multiple of the wavelength. These states allow for a high-fidelity preparation and minimally invasive readout in state-of-the-art setups. In particular, we suggest an experimental implementation using a coplanar waveguide coupled to superconducting transmon qubits on a chip. With minimal free space and intrinsic losses, virtually perfect dark states can be achieved for a low number of qubits featuring fast preparation and precise manipulation.

Coherent Control of Collective Spontaneous Emission through Self-Interference

As one of the central topics in quantum optics, collective spontaneous emission such as superradiance has been realized in a variety of systems. This Letter proposes an innovative scheme to coherently control collective emission rates via a self-interference mechanism in a nonlinear waveguide setting. The self-interference is made possible by photon backward scattering incurred by quantum scatterers in a waveguide working as quantum switches. Whether the interference is constructive or destructive is found to depend strongly on the distance between the scatterers and the emitters. The interference between two propagation pathways of the same photon leads to controllable superradiance and subradiance, with their collective decay rates much enhanced or suppressed (also leading to hyperradiance or population trapping). Furthermore, the self-interference mechanism is manifested by an abrupt change in the emission rates in real time. An experimental setup based on superconducting transmission line resonators and transmon qubits is further proposed to realize controllable collective emission rates.

Tailoring the superradiant and subradiant nature of two coherently coupled quantum emitters

The control and manipulation of quantum-entangled states is crucial for the development of quantum technologies. A promising route is to couple solid-state quantum emitters through their optical dipole-dipole interactions. Entanglement in itself is challenging, as it requires both nanometric distances between emitters and nearly degenerate electronic transitions. Here we implement hyperspectral imaging to identify pairs of coupled dibenzanthanthrene molecules, and find distinctive spectral signatures of maximally entangled superradiant and subradiant electronic states by tuning the molecular optical resonances with Stark effect. We demonstrate far-field selective excitation of the long-lived subradiant delocalized state with a laser field tailored in amplitude and phase. Optical nanoscopy of the coupled molecules unveils spatial signatures that result from quantum interferences in their excitation pathways and reveal the location of each emitter. Controlled electronic-states superposition will help deciphering more complex physical or biological mechanisms governed by the coherent coupling and developing quantum information schemes.

Efficient nano-photonic antennas based on dark states in quantum emitter rings

Nanoscopic arrays of quantum emitters can feature highly sub-radiant collective excitations with a lifetime exponentially growing with emitter number. Adding an absorptive impurity as an energy dump in the center of a ring shaped polygon allows to exploit this feature to create highly efficient single photon antennas. Here among regular polygons with an identical center absorbing emitter, a nonagon exhibits a distinct optimum of the absorption efficiency. This special enhancement originates from the unique emergence of a subradiant eigenstate with dominant center occupation. Only for nine emitters the sum of coupling strengths of each emitter to all others matches the center to the ring coupling. Analogous to a parabolic mirror the antenna ring then concentrates incoming radiation at its center without being significantly excited itself. Similar large efficiency enhancements, which even prevail for broadband excitation, can also be engineered for other antenna sizes by tailoring the frequency and magnitude of the central absorber. Interestingly, for very small structures a quantum treatment predicts an even stronger enhancement for the single photon absorption enhancement than a classical dipole model. As natural light harvesting structures are often based on ring shaped structures, the underlying principle might be exploited there as well.

Optical cooperative effects of multiemitters in a one-dimensional (1D) dense array

We theoretically explore cooperative effects of equally spaced multiemitters in a 1D dense array driven by a low-intensity probe field propagating through a 1D waveguide by modeling the emitters as point-like coupled electric dipoles. We calculate the collective optical spectra of a number of 1D emitter arrays with any radiation-retention coefficient η using both exact classical-electrodynamics and mean-field-theory formalisms. We illustrate cooperative effects of lossless 1D emitter arrays with η = 1 at the emitter spacings, which are displayed by steep edges accompanied by a deep minimum and Fano resonances in the plots of transmissivities as a function of the detuning of the incident light from the emitter resonance. Numerical simulation of the full width of such optical bandgaps reveals that cooperativity between emitters is greater in a small array of size N ≤ 8 than in a larger one of size N > 8. For a lossy 1D emitter array in which the radiation retention coefficient is equal to or less than 0.1 the transmissivity obtained by exact-electrodynamics scheme exhibits no bandgap structures, being in good agreement with the mean-field-theory result. We propose that a 1D multiemitter array may work as a nanoscale filter blocking transmission of light with a frequency in the range of optical bandgaps.

Active Control of Nanodielectric-Induced THz Quasi-BIC in Flexible Metasurfaces: A Platform for Modulation and Sensing

A bound state in the continuum (BIC) is a nonradiating state of light embedded in the continuum of propagating modes providing drastic enhancement of the electromagnetic field and its localization at micro-nanoscale. However, access to such modes in the far-field requires symmetry breaking. Here, it is demonstrated that a nanometric dielectric or semiconductor layer, 1000 times thinner than the resonant wavelength (λ/1000), induces a dynamically controllable quasi-bound state in the continuum (QBIC) with ultrahigh quality factor in a symmetric metallic metasurface at terahertz frequencies. Photoexcitation of nanostrips of germanium activates ultrafast switching of a QBIC resonance with 200% transmission intensity modulation and complete recovery within 7 ps on a low-loss flexible substrate. The nanostrips also form microchannels that provide an opportunity for BIC-based refractive index sensing. An optimization model is presented for (switchable) QBIC resonances of metamaterial arrays of planar symmetric resonators modified with any (active) dielectric for inverse metamaterial design that can serve as an enabling platform for active micro-nanophotonic devices.

Subradiant Emission from Regular Atomic Arrays: Universal Scaling of Decay Rates from the Generalized Bloch Theorem

The Hermitian part of the field-mediated dipole-dipole interaction in infinite periodic arrays of two-level atoms yields an energy band of the singly excited states. In this Letter, we show that a dispersion relation, ω_{k}-ω_{k_{ex}}∝(k-k_{ex})^{s}, near the band edge of the infinite system leads to the existence of subradiant states of finite one-dimensional arrays of N atoms with decay rates scaling as N^{-(s+1)}. This explains the recently discovered N^{-3} scaling and it leads to the prediction of power law scaling with higher power for special values of the lattice period. For the quantum optical implementation of the Su-Schrieffer-Heeger topological model in a dimerized emitter array, the band gap closing inherent to topological transitions changes the value of s in the dispersion relation and alters the decay rates of the subradiant states by many orders of magnitude.

Optical Magnetism and Huygens' Surfaces in Arrays of Atoms Induced by Cooperative Responses

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 Huygens' surface with the full 2π phase control of the transmitted light that allows for extreme wavefront engineering even at a single photon level. We illustrate this by creating a superposition of two different orbital angular momentum states of light from an ordinary input state that has no orbital angular momentum.

Light reflection and transmission in planar lattices of cold atoms

Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Here we present a theoretical scheme that enables efficient computation of collective optical responses of mono- and bi-layer planar square lattices of dense, cold two-level atoms using classical electrodynamics of coupled dipoles in the limit of low laser intensity. The steady-state transmissivity and reflectivity are obtained at a field point far away from the atomic lattices in the regime with no Bragg reflection. While our earlier method was based on exact solution of the electrodynamics for a small-scale lattice, here we calculate the dipole moments assuming that they are the same at all lattice sites, as for an infinite lattice. Atomic lattices with effectively over one hundred times more sites than in our earlier exact computations can then be simulated numerically with fewer computational resources. We have implemented an automatic selection of the number of sites under the given convergence criteria. We compare the numerical results from both computational schemes. We also find similarities and differences of a stack of two atomic lattices from a two-atom sample. Such aspects may be exploited to engineer a stack for potential applications.

Inelastic Scattering of Photon Pairs in Qubit Arrays with Subradiant States

We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded into a waveguide. Our analysis reveals a strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering, such as superradiant, subradiant, and twilight states, as a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to storage and processing of quantum information.

Adjusting Electric Field Intensity Using Hybridized Dielectric Metamolecule

In this paper, we report on achieving the hybridization effect in a Mie-based dielectric metamolecule and provide its physically intuitive picture. Hybridization results in the splitting of the initial overlapping resonance dips, thus leading to two new collective resonance modes. It was observed via the simulated displacement field distribution that the two modes behave as the in-phase and out-of-phase oscillation of two meta-atoms, thus enhancing and suppressing the intensity of the electric field at the gap between two meta-atoms. Moreover, since the two hybridized modes are caused by the interaction effect, the intensities of the electric field can be adjusted by several external factors, like applied forces and temperature. Taking advantage of this easy-equipped dielectric meta-device, certain zones in it can be applied to receive amplified signals and shielded noises of different frequencies in microwave communication fields. Moreover, due to the function of enhancing electric field intensities, it is also promising in wireless charging technology.

Demonstration of group delay above 40 ps at terahertz plasmon-induced transparency windows

Herein, we demonstrate one of the highest terahertz group delay of 42.4 ps achieved experimentally at 0.23 THz, on a flexible planar metamaterial. The unit cell of metasurface is made up of a textured closed cavity and another experimentally concentric metallic arc. By tuning the central angle of the metallic arc, its intrinsic dipolar mode is in destructive interference with the spoof localized surface plasmon (SLSP) on textured closed cavity, which results in a plasmon-induced transparency phenomenon. The measured transmittances of as-fabricated samples using terahertz-time domain spectroscopy validate numerical results using extended coupled Lorentz oscillator model. It is found that the coupling coefficient and damping ratio of SLSP relies on the radius of the ring structure of textured closed cavity. As a consequence, the slow light maximum values become manoeuverable in strength at certain frequencies of induced transparency windows. To the best of our knowledge, our experimental result is currently the highest value demonstrated so far within metasurface at terahertz band.

Nonlocal collective ultrastrong interaction of plasmonic metamaterials and photons in a terahertz photonic crystal cavity

Light-matter interaction in the strong coupling regime is of profound interest for fundamental quantum optics, information processing and the realization of ultrahigh-resolution sensors. Here, we report a new way to realize strong light-matter interaction, by coupling metamaterial plasmonic "quasi-particles" with photons in a photonic cavity, in the terahertz frequency range. The resultant cavity polaritons exhibit a splitting which can reach the ultra-strong coupling regime, even with the comparatively low density of quasi-particles, and inherit the high Q-factor of the cavity despite the relatively broad resonances of the Swiss-cross and split-ring-resonator metamaterials used. We also demonstrate nonlocal collective interaction of spatially separated metamaterial layers mediated by the cavity photons. By applying the quantum electrodynamic formalism to the density dependence of the polariton splitting, we can deduce the intrinsic transition dipole moment for single-quantum excitation of the metamaterial quasi-particles, which is orders of magnitude larger than those of natural atoms. These findings are of interest for the investigation of fundamental strong-coupling phenomena, but also for applications such as ultra-low-threshold terahertz polariton lasing, voltage-controlled modulators and frequency filters, and ultra-sensitive chemical and biological sensing.

Theory of Subradiant States of a One-Dimensional Two-Level Atom Chain

Recently, the subradiant states of one-dimensional two-level atom chains coupled to light modes were found to have decay rates obeying a universal scaling, and an unexpected fermionic character of the multiply excited subradiant states was discovered. In this Letter, we theoretically obtain the singly excited subradiant states, and by eliminating the superradiant modes, we demonstrate a relation between the multiply excited subradiant states and the Tonks-Girardeau limit of the Lieb-Liniger model which explains the fermionic behavior. In addition, we identify a new family of subradiant states with correlations different from the fermionic ansatz.

Super- and sub-radiance from two-dimensional resonant dipole-dipole interactions

We theoretically investigate the super- and sub-radiance from the resonant dipole-dipole interactions (RDDI) in a confined two-dimensional (2D) reservoir. The distinctive feature of 2D RDDI shows qualitatively and quantitatively different long-range behavior from RDDI in free space. We investigate the collective radiation properties of the singly-excited symmetric state under this 2D RDDI. This state also allows subradiant decays in much longer distances than the transition wavelength, showing longrange atom-atom correlations. We further study the dynamics of the subradiant states which can be accessed by imprinting spatially dependent phases on the atomic arrays. Our results demonstrate rich opportunities in engineering light-matter interactions in a confined 2D reservoir, and hold promise in applications of quantum light storage and single-excitation state manipulations.

Point-dipole approximation for small systems of strongly coupled radiating nanorods

Systems of closely-spaced resonators can be strongly coupled by interactions mediated by scattered electromagnetic fields. In large systems the resulting response has been shown to be more sensitive to these collective interactions than to the detailed structure of individual resonators. Attempts to describe such systems have resulted in point-dipole approximations to resonators that are computationally efficient for large resonator ensembles. Here we provide a detailed study for the validity of point dipole approximations in small systems of strongly coupled plasmonic nanorods, including the cases of both super-radiant and subradiant excitations, where the characteristics of the excitation depends on the spatial separation between the nanorods. We show that over an appreciable range of rod lengths centered on 210 nm, when the relative separation kl in terms of the resonance wave number of light k satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$kl\gtrsim \pi /2$$\end{document}kl≳π/2, the point electric dipole model becomes accurate. However, when the resonators are closer, the finite-size and geometry of the resonators modifies the excitation modes, in particular the cooperative mode line shifts of the point dipole approximation begin to rapidly diverge at small separations. We also construct simplified effective models by describing a pair of nanorods as a single effective metamolecule.

Subradiant Bell States in Distant Atomic Arrays

We study collective "free-space" radiation properties of two distant single-layer arrays of quantum emitters as two-level atoms. We show that this system can support a long-lived Bell superposition state of atomic excitations exhibiting strong subradiance, which corresponds to a nonlocal excitation of the two arrays. We describe the preparation of these states and their application in quantum information as a resource of nonlocal entanglement, including deterministic quantum state transfer with high fidelity between the arrays representing quantum memories. We discuss experimental realizations using cold atoms in optical trap arrays with subwavelength spacing, and analyze the role of imperfections.

Observation of Subradiant Atomic Momentum States with Bose-Einstein Condensates in a Recoil Resolving Optical Ring Resonator

We experimentally investigate the formation of subradiant atomic momentum states in Bose-Einstein condensates inside a recoil resolving optical ring resonator according to the theoretical proposal of Cola, Bigerni, and Piovella. The atoms are pumped from the side with laser light that contains two frequency components. They resonantly drive cavity assisted Raman transitions between three discreet atomic momentum states. Within a few hundred microseconds, the system evolves into a stationary subradiant state. In this state, the condensate develops two density gratings suitable to diffract the two frequency components of the pump field into the resonator. Both components destructively interfere such that scattering is efficiently suppressed. A series of subradiant states for various amplitude ratios of the two pump components between 0 and 2.1 have been observed. The results are well explained with a three state quantum model in mean field approximation.

Cooperative light scattering from helical-phase-imprinted atomic rings

We theoretically investigate the light scattering of super- and subradiant states of an atomic ring prepared by single excitation with a photon which carries an orbital angular momentum (OAM). For excitations with linear polarizations, the helical phase imprinted (HPI) atomic ring presents a discrete C₄ rotational symmetry when number of atoms N = 4n with integers n, while for circular polarizations with arbitrary N, the continuous and C_N symmetries emerge for the super- and subradiant modes, respectively. The HPI superradiant modes predominantly scatter photons in the forward-backward direction, and the forward scattering can be further enhanced as atomic rings are stacked along the excitation direction. The HPI subradiant modes then preferentially scatter photons in the transversal directions, and when rings are stacked concentrically and on a plane, crossover from sub- to superradiance is observed which leads to splitting and localization of the far-field scattering patterns in the polar angle. The HPI super- and subradiant states are thus detectable through measuring the far-field radiation patterns, which further allow quantum storage and detection of a single photon with an OAM.

Directional subradiance from helical-phase-imprinted multiphoton states

We theoretically investigate the far-field scattering properties of multiphoton super- and subradiant states which can be prepared by multiphoton excitations with orbital angular momentum (OAM). Due to multiphoton interference, the far-field patterns of the subradiant modes show directional scattering along the excitation direction or transverse scattering with number of peaks equal to the number of atoms. When more atoms are involved, we consider structures of stacked and concentric rings, which respectively show enhanced directional scattering and smoothed emission patterns. Our scheme gives insights to prepare many-body subradiant states, and is potentially applicable to quantum storage of multiphoton with OAM. By designing atomic spatial distributions, these cooperative states can tailor the far-field emission properties, which is useful for light collections and quantum information manipulations.

Directional Dicke Subradiance with Nonclassical and Classical Light Sources

We investigate Dicke subradiance of N≥2 distant quantum sources in free space, i.e., the spatial emission patterns of spontaneously radiating noninteracting multilevel atoms or multiphoton sources, prepared in totally antisymmetric states. We find that the radiated intensity is marked by a full suppression of spontaneous emission in particular directions. In resemblance to the analogous, yet inverted, superradiant emission profiles of N distant two-level atoms prepared in symmetric Dicke states, we call the corresponding emission patterns directional Dicke subradiance. We further derive that higher-order intensity correlations of the light emitted by statistically independent thermal light sources display the same directional Dicke subradiant behavior and show that it stems from the same interference phenomenon as in the case of quantum sources. We finally present measurements of directional Dicke subradiance for N=2,…,5 distant thermal light sources corroborating the theoretical findings.

Cavity Antiresonance Spectroscopy of Dipole Coupled Subradiant Arrays

An array of N closely spaced dipole coupled quantum emitters exhibits super- and subradiance with characteristic tailorable spatial radiation patterns. Optimizing the emitter geometry and distance with respect to the spatial profile of a near resonant optical cavity mode allows us to increase the ratio between light scattering into the cavity mode and free space emission by several orders of magnitude. This leads to distinct scaling of the collective coherent emitter-field coupling vs the free space decay as a function of the emitter number. In particular, for subradiant states, the effective cooperativity increases much faster than the typical linear ∝N scaling for independent emitters. This extraordinary collective enhancement is manifested both in the amplitude and the phase profile of narrow collective antiresonances appearing at the cavity output port in transmission spectroscopy.