Publications

We consider theoretically the mechanisms to realize antibunching between photons scattered on an array of two-level atoms in a general electromagnetic environment. Our goal is antibunching that persists for times much longer than the spontaneous emission lifetime of an individual atom. We identify two mechanisms for such persistent antibunching. The first one is based on subradiant states of the atomic array and the second one does not require any subradiant states. We provide two specific examples of array parameters with optimized antibunching, based on an array in a free space and an array coupled to a waveguide.

We have developed a theory of parametric photon generation in the waveguides coupled to arrays of quantum emitters with temporally modulated resonance frequencies. Such generation can be interpreted as a dynamical Casimir effect. We demonstrate numerically and analytically how the emission directionality and photon-photon correlations can be controlled by the phases of the modulation. The emission spectrum is shown to be strongly dependent on the anharmonicity of the emitter potential. Single- and double-excited state resonances have been identified in the emission spectrum.

The ability to control the direction of scattered light is crucial to provide flexibility and scalability for a wide range of on-chip applications, such as integrated photonics, quantum information processing, and nonlinear optics. Tunable directionality can be achieved by applying external magnetic fields that modify optical selection rules, by using nonlinear effects, or interactions with vibrations. However, these approaches are less suitable to control microwave photon propagation inside integrated superconducting quantum devices. Here, we demonstrate on-demand tunable directional scattering based on two periodically modulated transmon qubits coupled to a transmission line at a fixed distance. By changing the relative phase between the modulation tones, we realize unidirectional forward or backward photon scattering. Such an in-situ switchable mirror represents a versatile tool for intra- and inter-chip microwave photonic processors. In the future, a lattice of qubits can be used to realize topological circuits that exhibit strong nonreciprocity or chirality.

We present the fundamental concepts for enhancing photon-pair generation through spontaneous parametric downconversion in nonlinear dielectric metasurfaces. We show that in metasurfaces with specially designed two-dimensional (2D) or one-dimensional (1D) nanopatterns, which support optical bound states in the continuum, the photon rate and spectral brightness can be enhanced by orders of magnitude when compared to unpatterned thin films. In the case of our 2D structure, the photon pairs are emitted close to the normal, while our 1D lattice can mediate emission in a broad angular pattern. We also identify the distinct physical mechanism of the enhancement associated with 2D hyperbolic transverse phase matching of the frequencies with nondegenerate photons. These results can provide a foundation for future advances in the development of ultraminiaturized quantum sources of entangled photons tailored for various applications.

We present a theoretical study of the quantum states of two repelling spinless particles in a one-dimensional tight-binding model with a simple periodic lattice and open boundary conditions. We demonstrate that, when the particles are not identical, their interaction drives nontrivial correlated two-particle states, such as bound states and edge states, and induces interaction-induced flat bands. We show that the localization of the center of mass of the two particles enforces the localization of their relative motion, which means formation of the bound states. While the considered system is Hermitian, an insight into the bound states is provided by an approximate effective non-Hermitian model for the relative motion that features the non-Hermitian skin effect.

We study theoretically driven quantum dynamics in periodic arrays of two-level qubits coupled to the waveguide. We demonstrate that strongly subradiant eigenstates of the master equation for the density matrix emerge under strong coherent driving for arrays with the anti-Bragg periods d=λ/4,3λ/4.... This happens even though are no such eigenstates at low driving powers and is directly manifested by long-living quantum correlations between the qubits.

We reveal that strongly enhanced generation of photon pairs with narrow frequency spectra and sharp angular correlations can be realised through spontaneous parametric down-conversion in metasurfaces. This is facilitated by creating meta-gratings through nano-structuring of nonlinear films of sub-wavelength thickness to support the extended bound state in the continuum resonances, associated with ultra-high Q-factors, at the biphoton wavelengths across a wide range of emission angles. Such spectral features of photons can be beneficial for various applications, including quantum imaging. Our modelling demonstrates a pronounced enhancement, compared to unpatterned films, of the total photon-pair generation rate normalized to the pump power reaching 1.75 kHz mW-1, which is robust with respect to the angular bandwidth of the pump, supporting the feasibility of future experimental realisations.

Waveguide quantum electrodynamics offers a wide range of possibilities to effectively engineer interactions between artificial atoms via a one-dimensional open waveguide. While these interactions have been experimentally studied in the few qubit limit, the collective properties of such systems for larger arrays of qubits in a metamaterial configuration has so far not been addressed. Here, we experimentally study a metamaterial made of eight superconducting transmon qubits with local frequency control coupled to the mode continuum of a waveguide. By consecutively tuning the qubits to a common resonance frequency we observe the formation of super- and subradiant states, as well as the emergence of a polaritonic bandgap. Making use of the qubits quantum nonlinearity, we demonstrate control over the latter by inducing a transparency window in the bandgap region of the ensemble. The circuit of this work extends experiments with one and two qubits toward a full-blown quantum metamaterial, thus paving the way for large-scale applications in superconducting waveguide quantum electrodynamics.

We study theoretically the spatial distribution of the polarizations in the array of resonant electromagnetic dipole emitters coupled to a one-dimensional waveguide. The ratchet effect manifests itself in the spatial asymmetry of the distribution of the emitter occupations along the array under symmetrical pumping from both sides. The occupation asymmetry is driven by the periodic modulation in time of the emitter resonance frequencies. We find numerically and analytically the optimal conditions for maximal asymmetry. We also demonstrate that the ratchet effect can be enhanced due to the formation of topological electromagnetic edge states, enabled by the frequency modulation. Our results apply to classical structures with coupled resonators or arrays of semiconductor quantum wells as well as quantum setups with waveguide-coupled natural or artificial atoms.

We theoretically study subradiant states in an array of atoms coupled to photons propagating in a one-dimensional waveguide focusing on the strongly interacting many-body regime with large excitation fill factor . We introduce a generalized many-body entropy of entanglement based on exact numerical diagonalization followed by a high-order singular value decomposition. This approach has allowed us to visualize and understand the structure of a many-body quantum state. We reveal the breakdown of fermionized subradiant states with increase of with the emergence of short-ranged dimerized antiferromagnetic correlations at the critical point and the complete disappearance of subradiant states at .

We study theoretically optomechanical damping and amplification spectra for vibrations interacting with excitonic polaritons in a zero-dimensional microcavity. We demonstrate that the spectra strongly depend on the ratio of the exciton-phonon and the photon-phonon coupling constants. The interference between these couplings enables a situation when optomechanical gain exists either only for a lower polaritonic resonance or only for an upper polaritonic resonance. Our results provide insight into the optomechanical interactions in various multimode systems, where several resonant oscillators, such as photons, plasmons, or excitons, are coupled to the same vibration mode.

Recent discoveries in topological physics hold promise for disorder-robust quantum systems and technologies. Topological states provide the crucial ingredient of such systems featuring increased robustness to disorder and imperfections. Here we use an array of superconducting qubits to engineer a one-dimensional topologically nontrivial quantum metamaterial. By performing microwave spectroscopy of the fabricated array, we experimentally observe the spectrum of elementary excitations. We reveal not only the single-photon topological states but also the bands of exotic bound photon pairs arising due to the inherent anharmonicity of qubits. Furthermore, we discuss the formation of the two-photon bound edge-localized state and confirm the topological origin of our model demonstrating disorder-robust behavior of photon-photon correlation function for the topological edge state. Our work provides an experimental implementation of the topological model with attractive photon-photon interaction in a quantum metamaterial.

We demonstrate mechanisms of reciprocity breaking in nonlinear optics driven by the toroidal dipole moment which characterizes nontrivial spatial distributions of spins in solids. Using high-resolution femtosecond spectroscopy at electronic resonances in the magnetoelectric antiferromagnet CuB2O4, we show that nonreciprocity reaches 100% for opposite magnetic fields due to the interference of nonlinear coherent sources of second harmonic generation originating from the toroidal dipole moment, applied magnetic field, and noncentrosymmetric crystal structure. The experimental results are corroborated by theoretical analysis based on the crystal and magnetic symmetry of CuB2O4. Our findings open degrees of freedom in nonlinear optics and pave the way for future nonreciprocal spin-optronic devices operating on the femtosecond timescale.

We study theoretically the second-order correlation function g(2)(t) for photons transmitted through a periodic Bragg-spaced array of superconducting qubits, coupled to a waveguide. We demonstrate that photon bunching and antibunching persist much longer than both radiative and nonradiative lifetimes of a single qubit. Due to the Borrmann effect, that is a strongly non-Markovian collective feature of light-qubit coupling inherent to the Bragg regime, the photon-photon correlations become immune to nonradiative dissipation. This persistence of quantum correlations opens new avenues for enhancing the performance of setups of waveguide quantum electrodynamics.

Strong coupling between two quanta of different excitations leads to the formation of a hybridized state that paves a way for exploiting new degrees of freedom to control phenomena with high efficiency and precision. A magnon polaron is the hybridized state of a phonon and a magnon, the elementary quanta of lattice vibrations and spin waves in a magnetically ordered material. A magnon polaron can be formed at the intersection of the magnon and phonon dispersions, where their frequencies coincide. The observation of magnon polarons in the time domain has remained extremely challenging because the weak interaction of magnons and phonons and their short lifetimes jeopardize the strong coupling required for the formation of a hybridized state. Here, we overcome these limitations by spatial matching of magnons and phonons in a metallic ferromagnet with a nanoscale periodic surface pattern. The spatial overlap of the selected phonon and magnon modes formed in the periodic ferromagnetic structure results in a high coupling strength which, in combination with their long lifetimes, allows us to find clear evidence of an optically excited magnon polaron. We show that the symmetries of the localized magnon and phonon states play a crucial role in the magnon polaron formation and its manifestation in the optically excited magnetic transients.

Recent years have seen a tremendous interest to atomically thin membranes such as graphene or monolayers of transition metal dichalcogenides. Owing to their light mass and strong optical resonances, such membranes have become a promising platform for nanoscale resonant optomechanics. However, the considerations of the light-membrane interaction have been mostly restricted to the well-known light pressure and heating. Here, we theoretically predict a fundamentally different optomechanical effect that is specific for membranes. Namely, we demonstrate that illumination of optically resonant membranes by a plane electromagnetic wave directly affects their mechanical tension. The induced optomechanical tension is anisotropic and, depending on the spectral detuning from the resonance, can be both positive and negative. In the latter case, it can overcome the bending rigidity of the membrane leading to transition to the crumpled phase. Our fundamental findings apply from manipulation of biological cell membranes to controllable furling and unfurling of solar sails.

We study topological properties of bound pairs of photons in spatially modulated qubit arrays (arrays of two-level atoms) coupled to a waveguide. While bound pairs behave like Bloch waves, they are topologically nontrivial in the parameter space formed by the center-of-mass momentum and the modulation phase, where the latter plays the role of a synthetic dimension. In a superlattice where each unit cell contains three two-level atoms (qubits), we calculate the Chern numbers for the bound-state photon bands, which are found to be (1,-2,1). For open boundary conditions, we find exotic topological bound-pair edge states with radiative losses. Unlike the conventional case of the bulk-edge correspondence, these novel edge modes not only exist in gaps separating the bound-pair bands but they also may merge with and penetrate into the bands. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.

We study theoretically the radiative lifetime of bound two-particle excitations in a waveguide with an array of two-level atoms, realizing a one-dimensional Dicke-like model. Recently, Zhang et al. have numerically found an unexpected sharp maximum of the bound pair lifetime when the array period d is equal to 1/12th of the light wavelength λ0 [Phys. Rev. Research 2, 013173 (2020)10.1103/PhysRevResearch.2.013173]. We uncover a rigorous transformation from the non-Hermitian Hamiltonian with the long-range radiative coupling to the nearest-neighbor coupling model with the radiative losses only at the edges. This naturally explains the puzzle of long lifetime: The effective mass of the bound photon pair also diverges for d=λ0/12, hampering an escape of photons through the edges. We also link the oscillations of the lifetime with the number of atoms to the nonmonotonous quasi-flat-band dispersion of the bound pair.

We study theoretically an extended Bose-Hubbard model with the spatially modulated interaction strength, describing a one-dimensional array of tunneling-coupled nonlinear cavities. It is demonstrated that the spatial modulation of the nonlinearity induces bound two-photon edge states. The formation of these edge states has been understood analytically in terms of nonlinear self-localization. Our results show that the number of excitations and the modulation period of the interaction affect the photonic quantum walks in the universal way and both promote the edge states.

We theoretically study Rydberg excitons in one-dimensional chains of traps in Cu2O coupled via the van der Waals interaction. The triplet of optically active p-shell states acts as an effective spin 1, and the interactions between the excitons are strongly spin dependent. We predict that the system has the topological Haldane phase with the diluted antiferromagnetic order, long-range string correlations, and finite excitation gap. We also analyze the effect of the trap geometry and interactions anisotropy on the Rydberg exciton spin states and demonstrate that a rich spin phase diagram can be realized showing high tunability of the Rydberg exciton platform.

We develop a multipolar theory of second-harmonic generation (SHG) by dielectric nanoparticles made of noncentrosymmetric materials with bulk quadratic nonlinearity. We specifically analyze two regimes of optical excitation: illumination by a plane wave and single-mode excitation, when the laser pump drives the magnetic dipole mode only. Considering two classes of nonlinear crystalline solids (dielectric perovskite material and III-V semiconductor), we apply a symmetry approach to derive selection rules for the multipolar composition of the nonlinear radiation. The developed description can be used for design of efficient nonlinear optical nanoantennas with reconfigurable radiation characteristics.

Tunable directional scattering is of paramount importance for operation of antennas, routing of light, and design of topologically protected optical states. For visible light scattered on a nanoparticle, the directionality could be provided by the Kerker effect, exploiting the interference of electric and magnetic dipole emission patterns. However, magnetic optical resonances in small sub-100-nm particles are relativistically weak. Here, we predict inelastic scattering with the unexpectedly strong tunable directivity up to 5.25 driven by a trembling of a small particle without any magnetic resonance. The proposed optomechanical Kerker effect originates from the vibration-induced multipole conversion. We also put forward an optomechanical spin-Hall effect, the inelastic polarization-dependent directional scattering. Our results uncover an intrinsically multipolar nature of the interaction between light and mechanical motion and apply to a variety of systems from cold atoms to two-dimensional materials to superconducting qubits. An application for engineering of chiral optomechanical coupling and nonreciprocal transmission at nanoscale is proposed.

Optical nanoantennas have shown a great capacity for efficient extraction of photons from the near to the far field, enabling directional emission from nanoscale single-photon sources. However, their potential for the generation and extraction of multi-photon quantum states remains unexplored. Here we experimentally demonstrate the nanoscale generation of two-photon quantum states at telecommunication wavelengths based on spontaneous parametric down-conversion in an optical nanoantenna. The antenna is a crystalline AlGaAs nanocylinder, possessing Mie-type resonances at both the pump and the bi-photon wavelengths, and when excited by a pump beam it generates photon pairs with a rate of 35 Hz. Normalized to the pump energy stored by the nanoantenna, this rate corresponds to 1.4 GHz/Wm, being 1 order of magnitude higher than conventional on-chip or bulk photon-pair sources. Our experiments open the way for multiplexing several antennas for coherent generation of multi-photon quantum states with complex spatial-mode entanglement and applications in free-space quantum communications and sensing.

We theoretically study the dissipative Bose–Hubbard model describing the array of tunneling-coupled cavities with non-conservative photon–photon interaction. The bound two-photon states are formed in this system either in the limited range of the center-of-mass wave vectors or in the full Brillouin zone, depending on the strength of the dissipative interaction. Transition between these two regimes is manifested as an exceptional point in the complex energy spectrum. This improves fundamental understanding of the interplay of non-Hermiticity and interactions in the quantum structures and can potentially be used for on-demand nonlinear light generation in photonic lattices.

Magneto-optical phenomena such as the Faraday and Kerr effects play a central role in controlling the polarization and intensity of optical fields propagating through a medium. Intensity effects in which the direction of light emission depends on the orientation of the external magnetic field are of particular interest, as they can be harnessed for routing light. Effects known so far for accomplishing such routing all control light emission along the axis parallel to the magnetic field. Here we report a new class of emission phenomena where directionality is established perpendicular to the externally applied magnetic field for light sources located in the vicinity of a surface. As a proof of principle for this effect, which we call transverse magnetic routing of light emission, we demonstrate the routing of emission for excitons in a diluted-magnetic-semiconductor quantum well. In hybrid plasmonic semiconductor structures, we observe significantly enhanced directionality of up to 60%.

We demonstrate that the parity-time (PT) symmetric interfaces formed between non-Hermitian amplifying ("gainy") and lossy topological crystals exhibit PT phase transitions separating phases of lossless and decaying/amplifying topological edge transport. The spectrum of these interface states exhibits exceptional points (EPs) separating (i) a PT symmetric real-valued regime with an evenly distributed wave function in both gainy and lossy domains and (ii) a PT broken complex-valued regime, in which edge states asymmetrically localize in one of the domains. Despite its complex-valued character, the edge spectrum remains gapless and connects complex-valued bulk bands through the EPs. We find that the regimes exist when the real edge spectrum is embedded into the bulk continuum without mixing, indicating that the edge states are protected against leakage into the bulk by the PT symmetry. Two exemplary PT symmetric systems, exhibiting valley and Chern topological phases, respectively, are investigated and the connection with the corresponding Hermitian systems is established. Interestingly, despite the complex bulk spectrum of the Chern insulator, the bulk-interface correspondence principle still holds, as long as the topological gap remains open. The proposed systems are experimentally feasible in photonics, which is evidenced by our rigorous full-wave simulations of PT symmetric silicon-based photonic graphene.

We propose a one-dimensional nonlinear system of coupled anharmonic oscillators that dynamically undergoes a topological transition switching from the disordered and topologically trivial phase to the nontrivial one due to the spontaneous symmetry breaking. The topological transition is accompanied by the formation of the topological interface state in the spectrum of linearized excitations of the equilibrium phase. Our findings thus highlight the potential of the nonlinear systems for hosting the topological phases and uncover a fundamental link between the spontaneous-symmetry-breaking mechanism and topological interface states.

Integrated photonics is a leading platform for quantum technologies including nonclassical state generation 1, 2, 3, 4, demonstration of quantum computational complexity 5 and secure quantum communications 6. As photonic circuits grow in complexity, full quantum tomography becomes impractical, and therefore an efficient method for their characterization 7, 8 is essential. Here we propose and demonstrate a fast, reliable method for reconstructing the two-photon state produced by an arbitrary quadratically nonlinear optical circuit. By establishing a rigorous correspondence between the generated quantum state and classical sum-frequency generation measurements from laser light, we overcome the limitations of previous approaches for lossy multi-mode devices 9, 10. We applied this protocol to a multi-channel nonlinear waveguide network and measured a 99.28±0.31% fidelity between classical and quantum characterization. This technique enables fast and precise evaluation of nonlinear quantum photonic networks, a crucial step towards complex, large-scale, device production.

Relying on the bandgap modes of a nonlinear periodic waveguide, we propose the concept of atom-mediated spontaneous parametric down-conversion, where photon-pairs are only generated with a single 2-level emitter present, creating a heralded excitation mechanism.

Parity-time (PT) symmetric interfaces between amplifying and lossy crystals support dissipationless edge states exhibiting gapless spectra in complex band structure if exceptional points (EPs) of edge states exist, which is verified by rigorous full-wave simulations in PT-symmetric photonic graphene.

We propose the concept of atom-mediated spontaneous parametric down-conversion, in which photon-pair generation can take place only in the presence of a single two-level emitter, relying on the bandgap evanescent modes of a nonlinear periodic waveguide. Using a guided signal mode, an evanescent idler mode, and an atom-like emitter with the idler’s transition frequency embedded in the structure, we find a heralded excitation mechanism, in which the detection of a signal photon outside the structure heralds the excitation of the embedded emitter. We use a rigorous Green’s function quantization method to model this heralding mechanism in a 1D periodic waveguide and determine its robustness against losses.

We use an empirical tight-binding approach to calculate electron and hole states in [111]-grown PbSe nanowires. We show that the valley-orbit and spin-orbit splittings are very sensitive to the atomic arrangement within the nanowire elementary cell and differ for [111] nanowires with microscopic D3d,C2h, and D3 symmetries. For the nanowire diameter below 4 nm the valley-orbit splittings become comparable with the confinement energies and the k·p method is inapplicable. Nanowires with the D3 point symmetry having no inversion center exhibit giant spin splitting E=αkz, linear in one-dimensional wave vector kz, with the constant α up to 1eVÅ.

We develop a rigorous theoretical framework to describe light-sound interaction in the laser-pumped periodic multiple-quantum-well structure accounting for hybrid phonon-polariton excitations, termed phonoritons. We show that phonoritons exhibit the pumping-induced synthetic magnetic field in the artificial "coordinate-energy" space that makes transmission of left- and right- going waves different. The sound transmission nonreciprocity allows one to use such phonoritonic crystals with realistic parameters as optically controlled nanoscale acoustic diodes.

Recently introduced field of topological photonics aims to explore the concepts of topological insulators for novel phenomena in optics. Here polymeric chains of subwavelength silicon nanodisks are studied and it is demonstrated that these chains can support two types of topological edge modes based on magnetic and electric Mie resonances, and their topological properties are fully dictated by the spatial arrangement of the nanoparticles in the chain. It is observed experimentally and described how theoretically topological phase transitions at the nanoscale define a change from trivial to nontrivial topological states when the edge mode is excited.

We develop a general theoretical framework of integrated paired photon-plasmon generation through spontaneous wave mixing in nonlinear plasmonic and metamaterial nanostructures, rigorously accounting for material dispersion and losses in the quantum regime through the electromagnetic Green function. We identify photon-plasmon correlations in layered metal-dielectric structures with 70% internal heralding quantum efficiency and reveal a novel mechanism of broadband generation enhancement due to topological transition in hyperbolic metamaterials.

Photonic structures offer unique opportunities for controlling light-matter interaction, including the photonic spin Hall effect associated with the transverse spin-dependent displacement of a light beam that propagates in specially designed optical media. However, due to small spin-orbit coupling, the photonic spin Hall effect is usually weak at the nanoscale. Here we suggest theoretically and demonstrate experimentally, in both optics and microwave experiments, the photonic spin Hall effect enhanced by topologically protected edge states in subwavelength arrays of resonant dielectric particles. Based on direct near-field measurements, we observe the selective excitation of the topological edge states controlled by the handedness of the incident light. Additionally, we reveal the main requirements to the symmetry of photonic structures to achieve the topology-enhanced spin Hall effect, and also analyse the robustness of the photonic edge states against the long-range coupling. (Figure presented.) .

The photon blockade is a hallmark of quantum light transport through a single two-level system that can accommodate only one photon. Here, we theoretically show that two-photon transmission can be suppressed even for a system of a large number of quantum dots in a cavity when the biexciton nonlinearity is taken into account. We reveal the nonmonotonous dependence of the second-order correlation function of the transmitted photons on the biexciton binding energy. The blockade is realized by proper tuning of the biexciton resonance that controls the collective superradiant modes.

We present the realization of an inhomogeneously poled nonlinear waveguide array for the generation of photon pairs with integrated pump filtering. The biphoton wavefunction produced from the device is characterized using reversed sum-frequency generation measurements.

We study the optical properties of arrays of ultrathin cobalt nanowires by means of the Brillouin scattering of light on magnons. We employ the Stokes/anti-Stokes scattering asymmetry to probe the circular polarization of a local electric field induced inside nanowires by linearly polarized light waves. We observe the anomalous polarization conversion of the opposite sign than that in a bulk medium or thick nanowires with a great enhancement of the degree of circular polarization attributed to the unconventional refraction in a nanowire medium. A rigorous simulation of the electric field polarization as a function of the wire diameter and spacing reveals the reversed polarization for a thin sparse wire array, in full quantitative agreement with experimental results.

Energy exchange between closely packed semiconductor quantum dots allows for long-range transfer of electronic energy and enables new functionalities of nanostructured materials with a huge application potential in photonics, optoelectronics, and photovoltaics. This is illustrated by impressive advances of quantum-dot solids based on nanocrystals (NCs) of direct bandgap materials, where this effect has been firmly established. Regretfully, the (resonant) energy transfer in close-packed ensembles of NCs remains elusive for silicon-the main material for electronic and photovoltaic industries. This is the subject of the present study in which we conclusively demonstrate this process taking place in dense dispersions of Si NCs in an SiO₂ matrix. Using samples with different NC configurations, we can directly determine the wavelength dependent energy transfer rate and show that it (i) can be modulated by material parameters, and (ii) decreases with the NCs size, and thus being consistent with the energy flow proceeding from smaller to larger NCs. This result opens the way to new applications of Si NCs, requiring energy transport and extraction. In particular, it forms a fundamental step toward development of an excitonic all-Si solar cell, operating in some analogy to polymer devices.

We report on the first experimental observation of topological edge states in zigzag chains of plasmonic nanodisks. We demonstrate that such edge states can be selectively excited with the linear polarization of the incident light, and visualize them directly by near-field scanning optical microscopy. Our work provides experimental verification of a novel paradigm for manipulating light at the nanoscale in topologically nontrivial structures.

We reveal that asymmetric plasmonic nanostructures can exhibit significantly different absorption and scattering properties for light that propagates in opposite directions, despite the conservation of total extinction. We analytically demonstrate that this is a consequence of nonorthogonality of eigenmodes of the system. This results in the necessity for modal interference with potential enhancement via Fano resonances. Based on our theory, we propose a stacked nanocross design whose optical response exhibits an abrupt change between absorption and scattering cross-sections for plane waves propagating in opposite directions. This work thereby proposes the use of Fano resonances to employ nanostructures for measuring and distinguishing optical signals coming from opposite directions.

We theoretically demonstrate the strong Purcell effect in ε-near-zero ultra-anisotropic uniaxial metamaterials with an elliptic isofrequency surface. Contrary to the hyperbolic metamaterials, the effect does not rely on the diverging density of states and evanescent waves. As a result, both the radiative decay rate and the far-field emission power are enhanced. The effect can be realized in the periodic layered metal-dielectric nanostructures with a complex unit cell containing two different metallic layers.

We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of the existence of edge states in a system with a nonzero reflection phase winding number is given. The method is illustrated for one- and two-dimensional photonic crystals of nontrivial topology.

We suggest a novel type of photonic topological edge states in zigzag arrays of dielectric nanoparticles based on optically induced magnetic Mie resonances. We verify our general concept by the proof-of-principle microwave experiments with dielectric spherical particles, and demonstrate, experimentally, the ability to control the subwavelength topologically protected electromagnetic edge modes by changing the polarization of the incident wave.

We present a theoretical study of the discrete Green's function for the two-dimensional metamaterial, realized as a transmission line array. We demonstrate that the Green's function possesses distinct ripples when the isofrequency contour is of hyperbolic shape. This effect is a characteristic nonlocal feature of the hyperbolic regime and is beyond the effective medium approximation.

We present theoretical and experimental study of resonant Brillouin scattering of excitonic polaritons in one-dimensional multiple-quantum-well structure. We obtain general analytical results for the scattering light spectra, valid for arbitrary quantum-well arrangement. Application of our theory to the specific case of short-period superlattice shows a perfect quantitative agreement with experimental results for the height, width, and position of the Brillouin scattering peaks and allows us to determine the energy, radiative, and nonradiative decay rates of quantum-well excitons. We reveal the signatures of excitonic polariton formation in the scattering spectra and show that the spectral width and height are strongly sensitive to the number of wells in the sample.

We present a theory of topological edge states in one-dimensional resonant photonic crystals with a compound unit cell. Contrary to the conventional electronic topological states, the modes under consideration are radiative; i.e., they decay in time due to the light escape through the structure boundaries. We demonstrate that the edge states survive despite their radiative decay and can be detected both in time- and frequency-dependent light reflection.

An electric dipole placed in an anisotropic medium experiences a torque due to the induced polarization of the medium. The torque tends to align the dipole in the appropriate direction determined by the medium properties. Here we present simple quantitative theory of this effect and predict splitting of the emission spectrum lines of the elementary quantum emitter in an anisotropic environment due to the self-induced torque.

The routing of light in a deep subwavelength regime enables a variety of important applications in photonics, quantum information technologies, imaging and biosensing. Here we describe and experimentally demonstrate the selective excitation of spatially confined, subwavelength electromagnetic modes in anisotropic metamaterials with hyperbolic dispersion. A localized, circularly polarized emitter placed at the boundary of a hyperbolic metamaterial is shown to excite extraordinary waves propagating in a prescribed direction controlled by the polarization handedness. Thus, a metamaterial slab acts as an extremely broadband, nearly ideal polarization beam splitter for circularly polarized light. We perform a proof of concept experiment with a uniaxial hyperbolic metamaterial at radio-frequencies revealing the directional routing effect and strong subwavelength λ/300 confinement. The proposed concept of metamaterial-based subwavelength interconnection and polarization-controlled signal routing is based on the photonic spin Hall effect and may serve as an ultimate platform for either conventional or quantum electromagnetic signal processing.

We present a robust approach for interpreting the physics of Fano resonances in planar oligomer structures of both metallic and dielectric nanoparticles. We reveal a key mechanism for Fano resonances by demonstrating that such resonances can be generated purely from the interference of nonorthogonal collective eigenmodes, which are clearly identified based on the coupled-dipole approximation. We prove analytically a general theorem to identify the number of collective eigenmodes that can be excited in ring-type nanoparticle oligomers and further demonstrate that no dark-mode excitation is necessary for the existence of Fano resonances in symmetric oligomers. As a consequence, we unify the understanding of Fano resonances for both plasmonic and all-dielectric oligomers.

Optical forces constitute a fundamental phenomenon important in various fields of science, from astronomy to biology. Generally, intense external radiation sources are required to achieve measurable effects suitable for applications. Here we demonstrate that quantum emitters placed in a homogeneous anisotropic medium induce self-torques, aligning themselves in the well-defined direction determined by an anisotropy, in order to maximize their radiation efficiency. We develop a universal quantum-mechanical theory of self-induced torques acting on an emitter placed in a material environment. The theoretical framework is based on the radiation reaction approach utilizing the rigorous Langevin local quantization of electromagnetic excitations. We show more than 2 orders of magnitude enhancement of the self-torque by an anisotropic metamaterial with hyperbolic dispersion, having negative ratio of permittivity tensor components, in comparison with conventional anisotropic crystals with the highest naturally available anisotropy.

The subject of the review is the diffraction of an electromagnetic wave on a periodic condensed matter where the Bragg condition is satisfied at the frequency of resonance excited in this medium. The Bragg systems known as resonant photonic crystals in general have been considered, and the propagation, reflection, transmission, and diffraction of electromagnetic radiation in different objects-(I) periodic quantum-well structures near the exciton resonance, (II) optical lattices of atoms cooled in a laser field, and (III) bulk crystals and multilayers with gamma-ray resonance intranuclear transitions-have been described in a unified context. The main attention has been paid to the steady-state linear diffraction, including resonant reflection and transmission, which is the best studied and allows a comparison of the three aforementioned systems with the aim of revealing specific characteristics and common features. A characteristic common property of the considered systems is the suppression of non-radiative channels and an inhomogeneous broadening of the resonance frequency. The second fundamental property of resonant photonic crystals is that the interaction of light with resonant excitation can occur in two regimes depending on the thickness of the sample. In the superradiant regime realized for a small number of resonant layers N (fine structures), the height of the peak and half-width of the reflection spectrum monotonically increase with increasing value of N. With a further increase in N, there occurs a transition to a photonic-crystal regime where the half-width of the reflection spectrum is saturated, which manifests itself in the form of an optical stop band. The theoretical description is illustrated by experimental spectra measured for all three resonant Bragg systems.

We demonstrate how the medium with the hyperbolic isofrequency surfaces in the wavevector space can be realized by two-dimensional artificial transmission lines. The peculiar character of wave propagation in such a hyperbolic medium is visualized by the study of the cross-like emission pattern of a current source. Our results are supported by the direct solution of the Kirchhoff equations and an analytical theory.

The main experimental results of studies of the photoluminescence of silicon nanocrystals and theoretical methods developed for the description of optical processes occurring in them are reviewed. Special attention is focused on silicon nanocrystals in the SiO₂ matrix that were the object of most of the studies. Two fundamental theoretical methods described in detail are the multiband effective-mass method and the tight-binding method which have found wide application in simulating various processes occurring in nanostructures. A phenomenological model for excitons self-trapped on the surface of oxidized silicon nanocrystals, which has been recently developed on the basis of experimental results obtained by femtosecond spectroscopy, is reported.

We demonstrate how to realize an indefinite media with hyperbolic isofrequency surfaces in wavevector space by employing two-dimensional metamaterial transmission lines. We classify different types of such media, and visualize the peculiar character of wave propagation by study of the cross-like emission pattern of a current source placed in the lattice center. Our results are supported by a solution of the Kirchhoff equations, an analytical theory, and experimental data.

We revisit the problem of the electromagnetic Green function for homogeneous hyperbolic media, where longitudinal and transverse components of the dielectric permittivity tensor have different signs. We analyze the dipole emission patterns for both dipole orientations with respect to the symmetry axis and for different signs of dielectric constants, and show that the emission pattern is highly anisotropic and has a characteristic crosslike shape: the waves are propagating within a certain cone and are evanescent outside this cone. We demonstrate the coexistence of the conelike pattern due to emission of the extraordinary TM-polarized waves and elliptical pattern due to emission of ordinary TE-polarized waves. We find a singular complex term in the Green function, proportional to the δ function and governing the photonic density of states and Purcell effect in hyperbolic media.

We demonstrate that confinement-induced intervalley splittings of electron energy levels in PbSe and PbS nanocrystals are sensitive to the arrangement of atoms within a nanocrystal. The splittings are strongly suppressed for stoichiometric nanocrystals of T _d point symmetry lacking a center of inversion as opposed to nonstoichiometric nanocrystals of O _h point symmetry having an inversion center. Our findings are supported by both atomistic sp3d5s ^* tight-binding calculations and a symmetry analysis.

We report results of time-resolved induced absorption (IA) spectroscopy on Si nanocrystals (Si NCs) embedded in a SiO ₂ matrix. In line with theoretical modeling, the IA amplitude decreases with probing photon energy, however only until a certain threshold value. For larger photon energies, an increase of IA is observed. This unexpected behavior is interpreted in terms of the self-trapped exciton state whose formation in Si NCs was put forward some time ago based on theoretical considerations. Here, we present a direct experimental confirmation of this supposition.

We study the phonon-assisted intraband relaxation of electrons and holes confined in Si nanocrystals. The rates of relaxation processes are calculated as functions of the nanocrystal size and of the temperature. It occurs that the main contribution to the relaxation is provided by the mechanism where a single acoustic and a number of optical phonons, which are necessary to compensate the energy difference between the quantized charge carrier levels, are involved. We show that the phonon-assisted transitions between neighboring, size-quantized levels occur typically on a picosecond time scale, but vary over several orders of magnitude with the nanocrystal size. This results in a multiexponential decay of the carrier populations averaged over an ensemble of the nanocrystals with a given size distribution. When the nanocrystal size is reduced and more than two phonons are required for the transition, there is a qualitative difference in the behavior of the transition probabilities between the electrons and the holes. Whereas the electron transition times strongly oscillate around approximately the same mean values in the picosecond range with some drops toward nanoseconds, there is a clearly pronounced tendency of the relaxation time increase into the nanosecond time range for the hole transitions when the nanocrystal size is decreased. The increase of the temperature leads to a moderate decrease of the relaxation times but does not change the picture qualitatively.

We study the radiative decay and Purcell effect for a finite-size dipole emitter placed in a homogeneous uniaxial medium. We demonstrate that the radiative rate is strongly enhanced when the signs of the medium longitudinal and transverse dielectric constants are opposite, and that the isofrequency contour corresponds to a hyperbolic medium. We reveal that the Purcell enhancement factor remains finite even in the absence of losses and that it depends on the emitter size.

Here we propose a possible mechanism of fast Er³⁺ ions excitation in SiO₂ matrix with Si nanocrystals. We show that the presence of Si nanocrystals allows for non-resonant optical pumping of erbium ions by virtual Auger transition, which is the second order process via an intermediate virtual state: the first step is the optical transition inside the Si NC, and the second one is Auger excitation of Er³⁺ ion accompanied by intraband transition of the confined carrier. This mechanism of excitation can take place when the energy of photon absorbed is larger than the sum of the confined electron-hole ground state energy and the excitation energy of Er³⁺ ion. We have calculated the excitation cross-section as a function of the excitation energy for erbium ions situated both inside and outside the NC. We show that virtually all Er³⁺ ions inside NCs can be excited directly into the first excited state ⁴I_13/2 (responsible for the 1.5 μm emission) by the laser pulse of duration 5-10 ns. The results obtained for ions located outside NCs demonstrate the efficiency of the virtual excitation Auger process for transition of erbium ions into the higher excited states. 1.5 μm PL appears in this case as a result of nonradiative relaxation of excited ions down to the ⁴I_13/2 state. Correspondingly, the rise time of the 1.5 μm PL should be about several microseconds. The cross-sections calculated demonstrate the efficiency of such Auger process.

A theory of optical emission of quantum dot arrays in quantum microcavities is developed. The regime of the strong coupling between the quantum dots and photonic mode of the cavity is considered. The quantum dots are modeled as two-level systems. In the low pumping (linear) regime the emission spectra are mainly determined by the superradiant mode where the effective dipoles of the dots oscillate in phase. In the nonlinear regime the superradiant mode is destroyed and the emission spectra are sensitive to the parity of quantum dot number. Further increase in the pumping results in the emission line narrowing being an evidence of the lasing regime.

We propose a Fröhlich-type electron-phonon interaction mechanism for carriers confined in a non-polar quantum dot surrounded by an amorphous polar environment. Carrier transitions under this mechanism are due to their interaction with the oscillating electric field induced by the local vibrations in the surrounding amorphous medium. We estimate the corresponding energy relaxation rate for electrons in Si nanocrystals embedded in a SiO₂ matrix as an example. When the nanocrystal diameter is larger than 4 nm then the gaps between the electron energy levels of size quantization are narrow enough to allow for transitions accompanied by emission of a single local phonon having the energy about 140 meV. In such Si/SiO₂ nanocrystals the relaxation time is in nanosecond range.

Emission spectra of quantum dot arrays in zero-dimensional microcavities are studied theoretically. It is shown that their form is determined by the competition between collective superradiant mode formation and inhomogeneous broadening. A random sources method is used to calculate the photoluminescence spectra from an nonresonant pumped microcavity, and a standard diagram technique is used to provide a microscopic justification for the random sources method. The emission spectra of a microcavity are analyzed taking into account the spread of exciton energy due to inhomogeneous distribution of quantum dots and tunneling between them. It is demonstrated that the luminescence spectra of strongly tunnel-coupled quantum dots are sensitive to the dot positions, and the collective mode can (under certain conditions) be stabilized by random tunneling links.

A detailed experimental and theoretical study of the linear and nonlinear optical properties of different Fibonacci-spaced multiplequantum- well structures is presented. Systematic numerical studies are performed for different average spacing and geometrical arrangement of the quantum wells. Measurements of the linear and nonlinear (carrier density dependent) reflectivity are shown to be in good agreement with the computational results. As the pump pulse energy increases, the excitation-induced dephasing broadens the exciton resonances resulting in a disappearance of sharp features and reduction in peak reflectivity.

The fabrication and characterization of light-emitting one-dimensional photonic quasicrystals based on excitonic resonances is reported. The structures consist of high-quality GaAs/AlGaAs quantum wells grown by molecular-beam epitaxy with wavelength-scale spacings satisfying a Fibonacci sequence. The polaritonic (resonant light-matter coupling) effects and light emission originate from the quantum well excitonic resonances. Measured reflectivity spectra as a function of detuning between emission and Bragg wavelength are in good agreement with excitonic polariton theory. Photoluminescence experiments show that active photonic quasicrystals, unlike photonic crystals, can be good light emitters: While their long-range order results in a stopband similar to that of photonic crystals, the lack of periodicity results in strong emission.

We propose a resonant one-dimensional quasicrystal, namely, a multiple quantum well (MQW) structure satisfying the Fibonacci-chain rule with the golden ratio between the long and short interwell distances. The resonant Bragg condition is generalized from the periodic to Fibonacci MQWs. A dispersion equation for exciton polaritons is derived in the two-wave approximation; the effective allowed and forbidden bands are found. The reflection spectra from the proposed structures are calculated as a function of the well number and detuning from the Bragg condition.

The optical spectra of resonant Bragg and quasi-Bragg quantum-well structures are studied theoretically. The existence of special frequencies in the reflectance and absorbance spectra at which the reflectance or absorbance does not depend on the number of quantum wells in a structure is explained analytically. It is shown that the reflectance and absorbance spectra of structures in which the quantum-well width substantially exceeds the exciton Bohr radius also contain special frequencies and that the smooth spectral component is determined primarily by the interaction of the light wave with the quantum-well ground-state exciton.