Observation of localized flat-band states in Kagome photonic lattices

Emergence of flat bands and ferromagnetic fluctuations via orbital-selective electron correlations in Mn-based kagome metal

Kagome lattice has been actively studied for the possible realization of frustration-induced two-dimensional flat bands and a number of correlation-induced phases. Currently, the search for kagome systems with a nearly dispersionless flat band close to the Fermi level is ongoing. Here, by combining theoretical and experimental tools, we present Sc3Mn3Al7Si5 as a novel realization of correlation-induced almost-flat bands in the kagome lattice in the vicinity of the Fermi level. Our magnetic susceptibility, 27Al nuclear magnetic resonance, transport, and optical conductivity measurements provide signatures of a correlated metallic phase with tantalizing ferromagnetic instability. Our dynamical mean-field calculations suggest that such ferromagnetic instability observed originates from the formation of nearly flat dispersions close to the Fermi level, where electron correlations induce strong orbital-selective renormalization and manifestation of the kagome-frustrated bands. In addition, a significant negative magnetoresistance signal is observed, which can be attributed to the suppression of flat-band-induced ferromagnetic fluctuation, which further supports the formation of flat bands in this compound. These findings broaden a new prospect to harness correlated topological phases via multiorbital correlations in 3d-based kagome systems.

Shadows of structured beams in lenslike media

The self-healing phenomenon of structured light beams has been comprehensively investigated for its important role in various applications including optical tweezing, superresolution imaging, and optical communication. However, for different structured beams, there are different explanations for the self-healing effect, and a unified theory has not yet been formed. Here we report both theoretically and experimentally a study of the self-healing effect of structured beams in lenslike media, this is, inhomogeneous lenslike media with a quadratic gradient index. By observing the appearance of a number of shadows of obstructed structured wave fields it has been demonstrated that their self-healing in inhomogeneous media are the result of superposition of fundamental traveling waves. We have found that self-healing of structured beams occurs in this medium and, interestingly enough, that the shadows created in the process present sinusoidal propagating characteristics as determined by the geometrical ray theory in lenslike media. This work provides what we believe to be a new inhomogenous environment to explain the self-healing effect and is expected to deepen understanding of the physical mechanism.

Multiple flatbands and localized states in photonic super-Kagome lattices

We demonstrate multiple flatbands and compact localized states (CLSs) in a photonic super-Kagome lattice (SKL) that exhibits coexistence of singular and nonsingular flatbands within its unique band structure. Specifically, we find that the upper two flatbands of an SKL are singular-characterized by singularities due to band touching with their neighboring dispersive bands at the Brillouin zone center. Conversely, the lower three degenerate flatbands are nonsingular and remain spectrally isolated from other dispersive bands. The existence of such two distinct types of flatbands is experimentally demonstrated by observing stable evolution of the CLSs with various geometrical shapes in a laser-written SKL. We also discuss the classification of the flatbands in momentum space, using band-touching singularities of the Bloch wave functions. Furthermore, we validate this classification in real space based on unit cell occupancy of the CLSs in a single SKL plaquette. These results may provide insights for the study of flatband transport, dynamics, and nontrivial topological phenomena in other relevant systems.

Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Optically-Induced Symmetry Switching in a Reconfigurable Kagome Photonic Lattice: From Flatband to Type-III Dirac Cones

We demonstrate the transition of band structure from flatband to type-III Dirac cones in an electromagnetically induced Kagome photonic lattice generated in a three-level Λ-type 85Rb atomic configuration both experimentally and theoretically. Such instantaneously reconfigurable Kagome photonic lattice with flatband is "written" by a strong coupling field possessing a Kagome intensity distribution, which can modulate the refractive index of atomic vapors in a spatially periodical manner under electromagnetically induced transparency. By introducing an additional one-dimensional periodic coupling field to cover any one set of the three inequivalent sublattices of the induced Kagome photonic lattice, the dispersion-less energy band can evolve into type-III Dirac cones with linear dispersion by easily manipulating the intensity of the one-dimensional field. Our results may pave a new route to engineer in situ reconfigurable photonic structures with type-III Dirac cones, which can act as promising platforms to explore the underlying physics and beam dynamics.

Multifunctional resonant wavefront-shaping meta-optics based on multilayer and multi-perturbation nonlocal metasurfaces

Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming wavefront. In optical metasurfaces, for example, the localized modes of individual meta-units govern the wavefront shape over a broad bandwidth, while nonlocal lattice modes extended over many unit cells support high quality-factor resonances. Here, we experimentally demonstrate nonlocal dielectric metasurfaces in the near-infrared that offer both spatial and spectral control of light, realizing metalenses focusing light exclusively over a narrowband resonance while leaving off-resonant frequencies unaffected. Our devices attain this functionality by supporting a quasi-bound state in the continuum encoded with a spatially varying geometric phase. We leverage this capability to experimentally realize a versatile platform for multispectral wavefront shaping where a stack of metasurfaces, each supporting multiple independently controlled quasi-bound states in the continuum, molds the optical wavefront distinctively at multiple wavelengths and yet stay transparent over the rest of the spectrum. Such a platform is scalable to the visible for applications in augmented reality and transparent displays.

Excited quantum anomalous and spin Hall effect: dissociation of flat-bands-enabled excitonic insulator state

Quantum anomalous Hall effect (QAHE) and quantum spin Hall effect (QSHE) are two interesting physical manifestations of 2D materials that have an intrinsic nontrivial band topology. In principle, they are ground-state equilibrium properties characterized by Fermi level lying in a topological gap, below which all the occupied bands are summed to a non-zero topological invariant. Here, we propose theoretical concepts and models of 'excited' QAHE (EQAHE) and EQSHE generated by dissociation of an excitonic insulator (EI) state with complete population inversion (CPI), a uniquemany-bodyground state enabled by two yin-yang flat bands (FBs) of opposite chirality hosted in a diatomic Kagome lattice. The two FBs have a trivial gap in between, i.e. the system is a trivial insulator in thesingle-particleground-state, but nontrivial gaps above and below, so that upon photoexcitation the quasi-Fermi levels of both electrons and holes will lie in a nontrivial gap achieved by the CPI-EI state, as demonstrated by exact diagonalization calculations. Then dissociation of singlet and triplet EI state will lead to EQAHE and EQSHE, respectively. Realizations of yin-yang FBs in real materials are also discussed.

Engineering of flat bands and Dirac bands in two-dimensional covalent organic frameworks (COFs): relationships among molecular orbital symmetry, lattice symmetry, and electronic-structure characteristics

Two-dimensional covalent organic frameworks (2D-COFs), also referred to as 2D polymer networks, display unusual electronic-structure characteristics, which can significantly enrich and broaden the fields of electronics and spintronics. In this Focus article, our objective is to lay the groundwork for the conceptual description of the fundamental relationships among the COF electronic structures, the symmetries of their 2D lattices, and the frontier molecular orbitals (MOs) of their core and linker components. We focus on monolayers of hexagonal COFs and use tight-binding model analyses to highlight the critical role of the frontier-MO symmetry, in addition to lattice symmetry, in determining the nature of the electronic bands near the Fermi level. We rationalize the intriguing feature that, when the core unit has degenerate highest occupied MOs [or lowest unoccupied MOs], the COF highest valence band [or lowest conduction band] is flat but degenerate with a dispersive band at a high-symmetry point of the Brillouin zone; the consequences of having such band characteristics are briefly described. Multi-layer and bulk 2D COFs are found to maintain the salient features of the monolayer electronic structures albeit with a reduced bandgap due to the interlayer coupling. This Focus article is thus meant to provide an effective framework for the engineering of flat and Dirac bands in 2D polymer networks.

Realizing Kagome Band Structure in Two-Dimensional Kagome Surface States of RV_{6}Sn_{6} (R=Gd, Ho)

We report angle resolved photoemission experiments on a newly discovered family of kagome metals RV_{6}Sn_{6} (R=Gd, Ho). Intrinsic bulk states and surface states of the vanadium kagome layer are differentiated from those of other atomic sublattices by the real-space resolution of the measurements with a small beam spot. Characteristic Dirac cone, saddle point, and flat bands of the kagome lattice are observed. Our results establish the two-dimensional (2D) kagome surface states as a new platform to investigate the intrinsic kagome physics.

Band evolution and Landau-Zener Bloch oscillations in strained photonic rhombic lattices

We investigate band evolution of chiral and non-chiral symmetric flatband photonic rhombic lattices by applying a strain along the diagonal direction, and thereby demonstrating Landau-Zener Bloch (LZB) oscillations in the presence of a refractive index gradient. The chiral and non-chiral symmetric rhombic lattices are obtained by adding a detuning to uniform lattices. For the chiral symmetric lattices, the middle flatband is perturbed due to the chiral symmetry breaking while a nearly flatband appears as the bottom band with the increase of strain-induced next-nearest-neighbor hopping. Consequently, LZB oscillations exhibit intriguing characteristics such as asymmetric energy transitions and almost complete suppression of the oscillations. Nevertheless, for the non-chiral symmetric lattices, flatband persists owing to the retained particle-hole symmetry and evolves into the bottom band. Remarkably, the band gap can be readily tuned, which allows controlling of the amplitude of Landau-Zener tunneling (LZT) rate and may lead to thorough LZT. Our analysis provides an alternative perspective on the generation of tunable flatband and may also bring insight to study the symmetry and topological characterization of the flatband.

Strain induced localization to delocalization transition on a Lieb photonic ribbon lattice

Ribbon lattices are kind of transition systems in between one and two dimensions, and their study is crucial to understand the origin of different emerging properties. In this work, we study a Lieb ribbon lattice and the localization-delocalization transition occurring due to a reduction of lattice distances (compression) and the corresponding flat band deformation. We observe how above a critical compression ratio the energy spreads out and propagates freely across the lattice, therefore transforming the system from being a kind of insulator into a conductor. We implement an experiment on a photonic platform and show an excellent agreement with the predicted phenomenology. Our findings suggest and prove experimentally the use of compression or mechanical deformation of lattices to switch the transport properties of a given system.

Talbot effect of an electromagnetically induced square photonic lattice assisted by a spatial light modulator

We demonstrate the Talbot effect of an electromagnetically induced square photonic lattice formed under the electromagnetically induced transparency (EIT) condition both experimentally and theoretically in a three-level ⁸⁵Rb atomic configuration. The two-dimensional lattice patterns result from the diffraction of a Gaussian probe field traveling through the vapor cell, in which the refractive index is modulated by a coupling field with a two-dimensional periodic intensity distribution generated by a spatial light modulator. The experimental observations are consistent with the theoretical predictions. This investigation not only provides a new avenue for producing desired electromagnetically induced photonic lattices beyond the commonly adopted multi-beam interfering method but also broadens studies of electromagnetically induced Talbot effect to two-dimensional space.

Localization-to-delocalization transition of light in frequency-tuned photonic moiré lattices

We demonstrate in a numerical manner the intriguing localization-to-delocalization transition of light in frequency-tuned photonic moiré lattices, both in the zero-order and the higher-order regimes of light waves. We present a different technique to realize the composite photonic lattices, by means of two relatively twisted sublattices with different modulated lattice constants. Even though various kinds of photonic patterns including the commensurable and the incommensurable lattices can be well constructed, the observed transition between the localization and the delocalization of light field is moiré angle-independent. This angle-insensitive property was not reported before, and cannot be achieved by those photonic moiré lattices that are all moiré angle-dependent. We reveal that the obtained phase transition of light is robust to the changes of refractive index modulation of the photonic lattices. Moreover, we reveal that the effect of moiré angle-independent transition of light can be extended to the higher-order vortex light field, hence allowing prediction, for the first time to our knowledge, of both the localization and the delocalization of the vortex light field in the photonic lattices.

Exotic Topological Bands and Quantum States in Metal-Organic and Covalent-Organic Frameworks

ConspectusMetal-organic and covalent-organic frameworks (MOFs/COFs) have been extensively studied for fundamental interests and their promising applications, taking advantage of their unique structural properties, i.e., high porosity and large surface-to-volume ratio. However, their electronic and magnetic properties have been somewhat overlooked because of their relatively poor performance as conductive and/or magnetic materials. Recent experimental breakthroughs in synthesizing two-dimensional (2D) π-conjugated MOFs/COFs with high conductivity and robust magnetism through doping have generated renewed and increasing interest in their electronic properties. Meanwhile, comprehensive theoretical studies of the underlying physical principles have led to discovery of many exotic quantum states, such as topological insulating states, which were only observed in inorganic systems. Especially, the diversity and high tunability of MOFs/COFs have provided a playground to explore novel quantum physics and quantum chemistry as well as promising applications.The band theory has empowered us to understand the most fundamental electronic properties of inorganic crystalline materials, which can also be used to better understand MOFs/COFs. The first obvious difference between the two is that instead of atomic orbitals residing at lattice sites of inorganic crystals, molecular orbitals of organic ligands are predominant in MOFs/COFs. The second key difference is that usually all atomic orbitals in an inorganic crystal are subject to one common group of lattice symmetry, while atomic orbitals of metal ion and molecular orbitals of different organic ligands in MOFs/COFs belong to different subgroups of lattice symmetries. Both these differences will impact the band structure of MOFs/COFs, in particular making it more complex. Consequently, which subset of bands are of most importance depends strongly on the location of Fermi level, i.e., electron counting and charge doping. Furthermore, there are usually two types of characteristic electrons coupled in MOFs, i.e., strongly correlated localized d and f electrons and diffusive s and p electrons, which interplay with lattice, orbital, and spin degrees of freedom, leading to more exotic topological and magnetic band structures.In this Account, we present an up-to-date review of recent theoretical developments to better understand the exotic band structures of MOFs/COFs. Starting from three fundamental 2D lattice models, i.e., honeycomb, Kagome, and Lieb lattices, exotic Dirac and flat bands as well as the intriguing topological quantum states they host, e.g., quantum spin Hall and quantum anomalous Hall states, are outlined. In addition to the single-lattice models, we further elaborate on combined lattice model Hamiltonians, which give rise to overlapping bands hosting novel quantum states, such as nodal-line Dirac semimetal and unconventional superconducting states. Also, first-principles predictions of candidate MOFs/COFs that host these exotic bands and hence quantum phases are reviewed, which greatly extends the pool of materials beyond inorganic crystals for hosting exotic band structures.

Localized modes in a two-dimensional lattice with a pluslike geometry

We investigate analytically and numerically the existence and dynamical stability of different localized modes in a two-dimensional photonic lattice comprising a square plaquette inscribed in the dodecagon lattices. The eigenvalue spectrum of the underlying linear lattice is characterized by a net formed of one flat band and four dispersive bands. By tailoring the intersite coupling coefficient ratio, opening of gaps between two pairs of neighboring dispersive bands can be induced, while the fully degenerate flat band characterized by compact eigenmodes stays nested between two inner dispersive bands. The nonlinearity destabilizes the compact modes and gives rise to unique families of localized modes in the newly opened gaps, as well as in the semi-infinite gaps. The governing mechanism of mode localization in that case is the light energy self-trapping effect. We have shown the stability of a few families of nonlinear modes in gaps. The suggested lattice model may serve for probing various artificial flat-band systems such as ultracold atoms in optical lattices, periodic electronic networks, and polariton condensates.

Direct Observation of Flatband Loop States Arising from Nontrivial Real-Space Topology

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.

Critical topological nodal points and nodal lines/rings in Kagome graphene

Critical topological phases, possessing flat bands, provide a platform to study unique topological properties and transport phenomena under a many-body effect. Here, we propose that critical nodal points and nodal lines or rings can be found in Kagome lattices. After the C3 rotation symmetry of a single-layer Kagome lattice is eliminated, a quadratic nodal point splits into two critical nodal points. When the layered Kagome lattices are stacked into a three-dimensional (3D) structure, critical nodal lines or rings can be generated by tuning the interlayer coupling. Furthermore, we use Kagome graphene as an example to identify that these critical phases could be obtained in real materials. We also discuss flat-band-induced ferromagnetism. It is found that the flat band splits into two spin-polarized bands by hole-doping, and as a result the Dirac-type critical phases evolve into Weyl-type phases.

Partial quantum revivals of localized condensates in distorted lattices

We report on a peculiar propagation of bosons loaded by a short Laguerre-Gaussian pulse in a nearly flat band of a lattice potential. Taking a system of exciton polaritons in a kagome lattice as an example, we show that an initially localized condensate propagates in a specific direction in space, if anisotropy is taken into account. This propagation consists of quantum jumps, collapses, and revivals of the whole compact states, and it persists given any direction of anisotropy. This property reveals its signatures in the tight-binding model, and, surprisingly, it is much more pronounced in a continuous model. Quantum revivals are robust to the repulsive interaction and finite lifetime of the particles. Since no magnetic field or spin-orbit interaction is required, this system provides a new kind of easily implementable optical logic.

Methods for the construction of interacting many-body Hamiltonians with compact localized states in geometrically frustrated clusters

Adding interactions to many-body Hamiltonians of geometrically frustrated lattices often leads to diminished subspaces of localized states. In this paper, we show how to construct interacting many-body Hamiltonians, starting from the non-interacting tight-binding Hamiltonians, that preserve or even expand these subspaces. The methods presented involve modifications in the one-body network representation of the many-body Hamiltonians which generate new interacting terms in these Hamiltonians. The subspace of many-particle localized states can be preserved in the interacting Hamiltonian, by projecting the interacting terms onto the subspace of many-body extended states or by constructing the interacting Hamiltonian applying origami rules to the network. Expanded subspaces of localized states are found if interacting terms that mix subspaces with different number of particles are introduced. Furthermore, we present numerical methods for the determination of many-body localized states that allows one to address larger clusters and larger number of particles than those accessible by full diagonalization of the interacting Hamiltonian. These methods rely on the generalization of the concept of compact localized state in the network. Finally, we suggest a method to determine localized states that use a considerable fraction of the network.

Compact Localized States in Engineered Flat-Band [Formula: see text] Metamaterials

The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ([Formula: see text]) symmetric metamaterials comprised of split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this paradigmatic system, in which the SRRs are coupled through both electric and magnetic dipole-dipole forces, flat-bands may arise from tailoring its natural parameters (such as, e.g., the coupling coefficients between SRRs) and not from geometrical effects. For sets of parameters which values are tailored to flatten the upper band of the spectrum, the solution of the corresponding quadratic eigenvalue problem reveals the existence of compact, two-site localized eigenmodes. Numerical simulations confirm the existence and the dynamic stability of such modes, which can be formed through the evolution of single-site initial excitations without disorder or nonlinearity.

Asymmetric conical diffraction in dislocated edge-centered square lattices

We investigate linear and nonlinear evolution dynamics of light beams propagating along a dislocated edge-centered square lattice. The band structure and Brillouin zones of this novel lattice are analyzed analytically and numerically. Asymmetric Dirac cones as well as the corresponding Bloch modes of the lattice are obtained. By adopting the tight-binding approximation, we give an explanation of the asymmetry of Dirac cones. By utilizing the appropriate Bloch modes, linear and nonlinear asymmetric conical diffraction are demonstrated. We find that both the focusing and defocusing nonlinearities can enhance the asymmetry of the conical diffractions.

Photonic flat-band laser

Flat-band photonic lattices, i.e., arrays of waveguides or resonators displaying a flat Bloch band, offer new routes for light trapping and distortion-free imaging. Here it is shown that flat-band lattices can show stable and cooperative laser emission when optical gain is supplied to the system, despite the large degree of degeneracy of flat-band supermodes. By considering a quasi one-dimensional rhombic lattice of coupled semiconductor microrings, selective pumping of the outer sublattices can induce cooperative lasing in a supermode of the flat band.

Light propagation in binary kagome ribbons with evolving disorder

By introducing evolving disorder in the binary kagome ribbons, we study the establishment of diffusive spreading of flat band states characterized by diffractionless propagation in regular periodic ribbons. Our numerical analysis relies on controlling strength and rate of change of disorder during light propagation while tailoring binarism of the kagome ribbons in order to isolate the flat band with the gap from the rest of the ribbon's eigenvalue spectrum and study systematically its influence on diffusion. We show that the flat band plays a dominant role in the establishment of the diffusion for a given strength and rate of change of disorder, whereas the rest of the ribbon's eigenvalue spectrum induces only quantitative differences in the light spreading regimes. Due to the universality of studied phenomena, our findings may be of interest in various disordered physical systems with flat spectral bands, ranging from photonics to ultracold matter systems and plasmonics.

Flat bands and compactons in mechanical lattices

Local configurational symmetry in lattice structures may give rise to stationary, compact solutions, even in the absence of disorder and nonlinearity. These compact solutions are related to the existence of flat dispersion curves (bands). Nonlinearity can destabilize such compactons. One common flat-band-generating system is the one-dimensional cross-stitch model, in which compactons were shown to exist for the photonic lattice with Kerr nonlinearity. The compactons exist there already in the linear regime and are not generally destructed by that nonlinearity. Smooth nonlinearity of this kind does not permit performing complete stability analysis for this chain. We consider a discrete mechanical system with flat dispersion bands, in which the nonlinearity exists due to impact constraints. In this case, one can use the concept of the saltation matrix for the analytic construction of the monodromy matrix. Besides, we consider a smooth nonlinear lattice with linearly connected massless boxes, each containing two symmetric anharmonic oscillators. In this model, the flat bands and discrete compactons also readily emerge. This system also permits performing comprehensive stability analysis, at least in the anticontinuum limit, due to the reduced number of degrees of freedom. In both systems, there exist two types of localization. The first one is the complete localization, and the second one is the more common exponential localization. The latter type is associated with discrete breathers (DBs). Two principal mechanisms for the loss of stability are revealed. The first one is the possible internal instability of the symmetric and/or antisymmetric solution in the individual unit cell of the chain. One can interpret this instability pattern as internal resonance between the compacton and the DB. The other mechanism is global instability related to resonance of the stationary solution with the propagation frequencies. Different instability mechanisms lead to different bifurcations at the stability threshold.

Flat-band light dynamics in Stub photonic lattices

We experimentally study a Stub photonic lattice and excite their localized linear states originated from an isolated Flat Band at the center of the linear spectrum. By exciting these modes in different regions of the lattice, we observe that they do not diffract across the system and remain well trapped after propagating along the crystal. By using their wave nature, we are able to combine – in phase and out of phase – two neighbor states into a coherent superposition. These observations allow us to propose a novel setup for performing three different all-optical logical operations such as OR, AND, and XOR, positioning Flat Band systems as key setups to perform all-optical operations at any level of power.

Photonic crystal slow light waveguides in a kagome lattice

Slow light photonic crystal waveguides tightly compress propagating light and increase interaction times, showing immense potential for all-optical delay and enhanced light-matter interactions. Yet, their practical application has largely been limited to moderate group index values (<100), due to a lack of waveguides that reliably demonstrate slower light. This limitation persists because nearly all such research has focused on a single photonic crystal lattice type: the triangular lattice. Here, we present waveguides based on the kagome lattice that demonstrate an intrinsically high group index and exhibit slow and stopped light. We experimentally demonstrate group index values of >150, limited by our measurement resolution. The kagome-lattice waveguides are an excellent starting point for further slow light engineering in photonic crystal waveguides.

Controllable photon and phonon localization in optomechanical Lieb lattices

The Lieb lattice featuring flat band is not only important in strongly-correlated many-body physics, but also can be utilized to inspire new quantum devices. Here we propose an optomechanical Lieb lattice, where the flat-band physics of photon-phonon polaritons is demonstrated. The tunability of the band structure of the optomechanical arrays allows one to obtain an approximate photon or phonon flat band as well as the transition between them. This ultimately leads to the result that the controllable photon or phonon localization could be realized by the path interference effects. This study offers an alternative approach to explore the exotic photon and phonon many-body effects, which has potential applications in the future hybrid-photon-phonon quantum network and engineering new type solid-state quantum devices.

Single and double linear and nonlinear flatband chains: Spectra and modes

We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields. In the single-chain system, a full analysis is presented, first, for the single nonlinear cell, making it possible to find all stationary states, viz., antisymmetric, symmetric, and asymmetric ones, including an exactly investigated symmetry-breaking bifurcation of the subcritical type. In the nonlinear infinite single-component chain, compact localized states (CLSs) are found in an exact form too, as an extension of known compact eigenstates of the linear diamond chain. Their stability is studied by means of analytical and numerical methods, revealing a nontrivial stability boundary. In addition to the CLSs, various species of extended states and exponentially localized lattice solitons of symmetric and asymmetric types are also studied, by means of numerical calculations and variational approximation. As a result, existence and stability areas are identified for these modes. Finally, the linear version of the double diamond chain is solved in an exact form, producing two split flatbands in the system's spectrum.

Observation of robust flat-band localization in driven photonic rhombic lattices

We demonstrate that a flat-band state in a quasi-one-dimensional rhombic lattice is robust in the presence of external drivings along the lattice axis. The lattice was formed by periodic arrays of evanescently coupled optical waveguides, and the external drivings were realized by modulating the paths of the waveguides. We excited a superposition of flat-band eigenmodes at the input and observed that this state does not diffract in the presence of static, as well as high-frequency sinusoidal drivings. This robust localization is due to destructive interference of the analogous wavefunction and is associated with the symmetry in the lattice geometry. We then excited the dispersive bands and observed Bloch oscillations and coherent destruction of tunneling.

Observation of dipolar transport in one-dimensional photonic lattices

We experimentally study the transport properties of dipolar and fundamental modes on one dimensional (1D) coupled waveguide arrays. By carefully modulating a wide optical beam, we are able to effectively excite dipolar or fundamental modes to study discrete diffraction (single-site excitation) and gaussian beam propagation (multi-site excitation plus a phase gradient). We observe that dipolar modes experience a larger spreading area due to an effective larger coupling constant, which is found to be more than two times larger than the one for fundamental modes. Additionally, we study the effect of non-diagonal disorder and find that while fundamental modes are already trapped on a weakly disorder array, dipoles are still able to propagate across the system.