Observation of Period-Doubling Bloch Oscillations.

Bloch oscillations refer to the periodic oscillation of a wave packet in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wave packet traversing the first Brillouin zone once. Here, we demonstrate, both theoretically and experimentally, the optical Bloch oscillations where the wave packet must traverse the first Brillouin zone twice to complete a full cycle, resulting in a period of oscillation that is 2 times longer than that of usual Bloch oscillations. The unusual Bloch oscillations arise due to the band crossing of valley-Hall topological edge states at the Brillouin boundary for zigzag domain walls between two staggered honeycomb lattices with inverted on-site energy detuning, which are protected by the glide-reflection symmetry of the underlying structures. Our work sheds light on the direct detection of band crossings resulting from intrinsic symmetries that extend beyond the fundamental translational symmetry in topological systems.

Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions.

We study the nonlinear optical properties of heterojunctions made of graphene nanoribbons (GNRs) consisting of two segments with either the same or different topological properties. By utilizing a quantum mechanical approach that incorporates distant-neighbor interactions, we demonstrate that the presence of topological interface states significantly enhances the second- and third-order nonlinear optical response of GNR heterojunctions that are created by merging two topologically inequivalent GNRs. Specifically, GNR heterojunctions with topological interface states display third-order harmonic hyperpolarizabilities that are more than two orders of magnitude larger than those of their similarly sized counterparts without topological interface states, whereas the second-order harmonic hyperpolarizabilities exhibit a more than ten-fold contrast between heterojunctions with and without topological interface states. Additionally, we find that the topological state at the interface between two topologically distinct GNRs can induce a noticeable red-shift of the quantum plasmon frequency of the heterojunctions. Our results reveal a general and profound connection between the existence of topological states and an enhanced nonlinear optical response of graphene nanostructures and possible other photonic systems.

Vector valley Hall edge solitons in distorted type-II Dirac photonic lattices.

Topological edge states have recently garnered a lot of attention across various fields of physics. The topological edge soliton is a hybrid edge state that is both topologically protected and immune to defects or disorders, and a localized bound state that is diffraction-free, owing to the self-balance of diffraction by nonlinearity. Topological edge solitons hold great potential for on-chip optical functional device fabrication. In this report, we present the discovery of vector valley Hall edge (VHE) solitons in type-II Dirac photonic lattices, formed by breaking lattice inversion symmetry with distortion operations. The distorted lattice features a two-layer domain wall that supports both in-phase and out-of-phase VHE states, appearing in two different band gaps. Superposing soliton envelopes onto VHE states generates bright-bright and bright-dipole vector VHE solitons. The propagation dynamics of such vector solitons reveal a periodic change in their profiles, accompanied by the energy periodically transferring between the layers of the domain wall. The reported vector VHE solitons are found to be metastable.

Two-dimensional Thouless pumping of light in photonic moiré lattices.

Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this phenomenon manifests itself in the magnitude and direction of shift of the beam center-of-mass averaged over one pumping cycle. Our experimental results are supported by systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of probe light beam in optically-induced photorefractive moiré lattice. Our system affords a powerful platform for the exploration of topological pumping in tunable commensurate and incommensurate geometries.

Two-Dimensional Nonlinear Thouless Pumping of Matter Waves.

We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.

Nonlinear Thouless Pumping: Solitons and Transport Breakdown.

One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold, the transfer of both dispersive wave packets and solitons occurs in accordance with the predictions of the linear theory; i.e., it is quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of the transport is also explained by nontrivial topology of the bands. In that case, the nonlinearity induces Rabi oscillations of atoms between two (or more) lowest bands. If the sum of the dynamical Chern numbers of the populated bands is zero, the oscillatory dynamics of a matter soliton in space occurs, which corresponds to the transport breakdown. Otherwise, the sum of the Chern numbers of the nonlinearity-excited bands determines the direction and magnitude of the average velocity of matter solitons that remain quantized and admit fractional values. Thus, even in the strongly nonlinear regime the topology of the linear bands is responsible for the evolution of solitons. The transition between different dynamical regimes is accurately described by the perturbation theory for solitons.

Mechanisms for Hiding Sensitive Genotypes with Information-Theoretic Privacy.

Motivated by the growing availability of personal genomics services, we study an information-theoretic privacy problem that arises when sharing genomic data: a user wants to share his or her genome sequence while keeping the genotypes at certain positions hidden, which could otherwise reveal critical health-related information. A straightforward solution of erasing (masking) the chosen genotypes does not ensure privacy, because the correlation between nearby positions can leak the masked genotypes. We introduce an erasure-based privacy mechanism with perfect information-theoretic privacy, whereby the released sequence is statistically independent of the sensitive genotypes. Our mechanism can be interpreted as a locally-optimal greedy algorithm for a given processing order of sequence positions, where utility is measured by the number of positions released without erasure. We show that finding an optimal order is NP-hard in general and provide an upper bound on the optimal utility. For sequences from hidden Markov models, a standard modeling approach in genetics, we propose an efficient algorithmic implementation of our mechanism with complexity polynomial in sequence length. Moreover, we illustrate the robustness of the mechanism by bounding the privacy leakage from erroneous prior distributions. Our work is a step towards more rigorous control of privacy in genomic data sharing.

Multifrequency Solitons in Commensurate-Incommensurate Photonic Moiré Lattices.

We predict that photonic moiré patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the pattern. The question addressed here is how the geometry affects the joint trapping of multiple parametrically coupled waves into a single soliton state. We show that above the localization-delocalization transition the threshold power for soliton excitation is drastically reduced relative to uniform media. Also, the geometry of the moiré pattern shifts the condition for phase matching between the waves to the value that matches the edges of the eigenmode bands, thereby shifting the properties of all soliton families. Moreover, the phase-mismatch bandwidth for soliton generation is dramatically broadened in the moiré patterns relative to latticeless structures.

Giant All-Optical Modulation of Second-Harmonic Generation Mediated by Dark Excitons.

All-optical control of nonlinear photonic processes in nanomaterials is of significant interest from a fundamental viewpoint and with regard to applications ranging from ultrafast data processing to spectroscopy and quantum technology. However, these applications rely on a high degree of control over the nonlinear response, which still remains elusive. Here, we demonstrate giant and broadband all-optical ultrafast modulation of second-harmonic generation (SHG) in monolayer transition-metal dichalcogenides mediated by the modified excitonic oscillation strength produced upon optical pumping. We reveal a dominant role of dark excitons to enhance SHG by up to a factor of ∼386 at room temperature, 2 orders of magnitude larger than the current state-of-the-art all-optical modulation results. The amplitude and sign of the observed SHG modulation can be adjusted over a broad spectral range spanning a few electronvolts with ultrafast response down to the sub-picosecond scale via different carrier dynamics. Our results not only introduce an efficient method to study intriguing exciton dynamics, but also reveal a new mechanism involving dark excitons to regulate all-optical nonlinear photonics.

Localization and delocalization of light in photonic moiré lattices.

Moiré lattices consist of two superimposed identical periodic structures with a relative rotation angle. Moiré lattices have several applications in everyday life, including artistic design, the textile industry, architecture, image processing, metrology and interferometry. For scientific studies, they have been produced using coupled graphene-hexagonal boron nitride monolayers1,2, graphene-graphene layers3,4 and graphene quasicrystals on a silicon carbide surface5. The recent surge of interest in moiré lattices arises from the possibility of exploring many salient physical phenomena in such systems; examples include commensurable-incommensurable transitions and topological defects2, the emergence of insulating states owing to band flattening3,6, unconventional superconductivity4 controlled by the rotation angle7,8, the quantum Hall effect9, the realization of non-Abelian gauge potentials10 and the appearance of quasicrystals at special rotation angles11. A fundamental question that remains unexplored concerns the evolution of waves in the potentials defined by moiré lattices. Here we experimentally create two-dimensional photonic moiré lattices, which-unlike their material counterparts-have readily controllable parameters and symmetry, allowing us to explore transitions between structures with fundamentally different geometries (periodic, general aperiodic and quasicrystal). We observe localization of light in deterministic linear lattices that is based on flat-band physics6, in contrast to previous schemes based on light diffusion in optical quasicrystals12, where disorder is required13 for the onset of Anderson localization14 (that is, wave localization in random media). Using commensurable and incommensurable moiré patterns, we experimentally demonstrate the two-dimensional localization-delocalization transition of light. Moiré lattices may feature an almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool for controlling the properties of light patterns and exploring the physics of periodic-aperiodic phase transitions and two-dimensional wavepacket phenomena relevant to several areas of science, including optics, acoustics, condensed matter and atomic physics.

Localization and Anderson delocalization of light in fractional dimensions with a quasi-periodic lattice.

We address the properties of wavepacket localization-delocalization transition (LDT) in fractional dimensions with a quasi-periodic lattice. The LDT point, which is generally determined by the competition between two sub-lattices comprising the quasi-periodic lattice, turns out to be inversely proportional to the Lévy index. Surprisingly, we find that, in the presence of weak structural disorder, anti-Anderson localization occurs, i.e., the introduced disorder results in an increasing of the size of the linear modes. Inclusion of a weak focusing nonlinearity is shown to improve localization. The propagation simulation achieves excellent agreement with the linear and nonlinear eigenmode analysis.

Coupling of Edge States and Topological Bragg Solitons.

The existence of the edge states at the interface between two media with different topological properties is protected by symmetry, which makes such states robust against structural defects or disorder. We show that, if a system supports more than one topological edge state at the interface, even a weak periodic deformation may scatter one edge state into another without coupling to bulk modes. This is the Bragg scattering of the edge modes, which in a topological system is highly selective, with closed bulk and backward scattering channels, even when conditions for resonant scattering are not satisfied. When such a system bears nonlinearity, Bragg scattering enables the formation of a new type of soliton-topological Bragg solitons. We report them in a spin-orbit-coupled (SOC) Bose-Einstein condensate in a homogeneous honeycomb Zeeman lattice. An interface supporting two edge states is created by two different SOCs, with the y component of the synthetic magnetic field having opposite directions at different sides of the interface. The reported Bragg solitons are found to be stable.

Surface modes in plasmonic Bragg fibers with negative average permittivity.

We investigate surface modes in plasmonic Bragg fibers composed of nanostructured coaxial cylindrical metal-dielectric multilayers. We demonstrate that the existence of surface modes is determined by the sign of the spatially averaged permittivity of the plasmonic Bragg fiber, ε¯. Specifically, localized surface modes occur at the interface between the cylindrical core with ε¯<0 and the outermost uniform dielectric medium, which is similar to the topologically protected plasmonic surface modes at the interface between two different one-dimensional planar metal-dielectric lattices with opposite signs of the averaged permittivity. Moreover, when increasing the number of dielectric-metal rings, the propagation constant of surface modes with different azimuthal mode numbers is approaching that of surface plasmon polaritons formed at the corresponding planar metal/dielectric interface. Robustness of such surface modes of plasmonic Bragg fibers is demonstrated as well.

Adaptive pumping for spectral control of broadband second-harmonic generation.

Second-harmonic generation (SHG) is always a significant frequency conversion process in nonlinear optics for many great applications but can be limited when broadband spectral laser sources are involved, e.g., femtosecond pulses. The conversion efficiency can be high, but the spectral control is hard because of the phase-matching (PM) limitation. Recently, a random quasi-phase-matching (QPM) scheme was proposed to make use of highly nonlinear materials that are difficult to be phase matched under traditional configurations. The spectral control is even harder in anisotropic random materials, and the coherence is completely lost. Here, we proposed an approach to solve this problem by coherent light control via feedback-based wavefront shaping. We utilized this method for spectral control of broadband SHG, which can be efficient even in strongly scattering media. Randomly selected wavelengths in the broadband spectra were enhanced with a good selectivity, and the direction was also controlled in a three-dimensional (3D) configuration. This technique paves the way for convenient spatial and spectral control of both linear and nonlinear emissions and a local enhancement of their conversion efficiency, indicating great progress in both random and ultrafast nonlinear optics.

Quantum anomalous Hall-quantum spin Hall effect in optical superlattices.

We consider the topological characteristics of the spin-orbital coupling particles loaded in one-dimensional (1D) optical superlattices subject to the Zeeman field. The phase shift of the superlattice provides a virtual dimension which allows us to simulate two-dimensional topological phases with a physically 1D system. The system possesses a variety of quantum phase transitions over a large parametric space and two important topological phases, namely, quantum anomalous Hall (QAH) and quantum spin Hall (QSH) phases are found to coexist in the system, but they reside in different bandgaps. This new category of gap-dependent QAH--QSH insulator paves the way for the possible observation of the coexistence of QSH and QAH effects at one platform.

Plasmonic topological insulators for topological nanophotonics.

Photonic topological insulators are optical structures supporting robust propagation of light at their edges that are topologically protected from scattering. Here we propose the concept of plasmonic topological insulators (PTI) that not only topologically protect light at the lattice edges but also enable their confinement and guidance at the deep-subwavelength scale. The suggested PTI are composed of an evanescently coupled array of metallic nanowires that are modulated periodically along the light propagation direction. The intrinsic loss associated with the PTI is found not to deteriorate their topological protection on the edge modes. The proposed PTI may find interesting applications in nanophotonics, where the tolerance to the fabrication disorders for device applications are essential.

Second-harmonic focusing by a nonlinear turbid medium via feedback-based wavefront shaping.

Scattering has usually been considered detrimental for optical focusing or imaging. Recently, more and more research has shown that strongly scattering materials can be utilized to focus coherent light by controlling or shaping the incident light. Here, purposeful focusing of second-harmonic waves, which are generated and scattered from nonlinear turbid media via feedback-based wavefront shaping, is presented. This Letter shows a flexible manipulation of both disordered linear and nonlinear scattering signals, indicating more controllable degrees of freedom for the description of turbid media. This technique also provides a possible way to an efficient transmission of nonlinear signal at a desired location in the form of a focal point or other patterns. With the combination of random nonlinear optics and wavefront shaping methods, more interesting applications can be expected in the future, such as nonlinear transmission matrix, multi-frequency imaging, and phase-matching-free nonlinear optics.

Localized waves supported by the rotating waveguide array.

We show that truncated rotating square waveguide arrays support new types of localized modes that exist even in the linear case, in complete contrast to localized excitations in nonrotating arrays requiring nonlinearity for their existence and forming above the energy flow threshold. These new modes appear either around an array center, since the rotation leads to the emergence of the effective attractive potential with a minimum at the rotation axis, or in the array corners, in which case localization occurs due to competition between the centrifugal force and total internal reflection at the interface of the truncated array. The degree of localization of the central and corner modes mediated by the rotation increases with the rotation frequency. The stable rotating soliton families bifurcating from linear modes are analyzed in both focusing and defocusing media.

Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials.

We introduce a composite optical lattice created by two mutually rotated square patterns and allowing observation of continuous transformation between incommensurate and completely periodic structures upon variation of the rotation angle θ. Such lattices acquire periodicity only for rotation angles cos θ = a/c, sin θ = b/c, set by Pythagorean triples of natural numbers (a, b, c). While linear eigenmodes supported by lattices associated with Pythagorean triples are always extended, composite patterns generated for intermediate rotation angles allow observation of the localization-delocalization transition of eigenmodes upon modification of the relative strength of two sublattices forming the composite pattern. Sharp delocalization of supported modes for certain θ values can be used for visualization of Pythagorean triples. The effects predicted here are general and also take place in composite structures generated by two rotated hexagonal lattices.

Topological surface plasmons in superlattices with changing sign of the average permittivity.

We address the topological properties of one-dimensional plasmonic superlattices composed of alternating metallic and dielectric layers. We reveal that the Zak phase of such plasmonic lattices is determined by the sign of the spatial average of their permittivity, ε¯, and as such the topology and their associated interfacial (edge) states are extremely robust against structural disorder. Our study shows that the topologically protected interfacial modes occurring at the interface between two plasmonic lattices with opposite signs of ε¯ can be viewed as the generalization of the conventional surface plasmon polaritons existing at metallic-dielectric interfaces.