Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices.

We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.

Quantum Hall Effect with Composites of Magnetic Flux Tubes and Charged Particles.

Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons-particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object with an intrinsic magnetic dipole moment is placed between two semi-infinite blocks of a high-permeability (µ_{r}) material, and the images of the magnetic moment create an effective flux tube. We show that the scheme can lead to a realization of Wilczek's anyons, when a two-dimensional electron system, which exhibits the integer quantum Hall effect, is sandwiched between two blocks of the high-µ_{r} material with a temporally fast response (in the cyclotron and Larmor frequency range). The signature of Wilczek's anyons is a slight shift of the resistivity at the plateau of the IQHE. Thus, the quest for high-µ_{r} materials at high frequencies, which is underway in the field of metamaterials, and the quest for anyons, are here found to be on the same avenue.

Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space.

We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases.

Construction of Topological Bound States in the Continuum Via Subsymmetry.

Topological bound states in the continuum (BICs) are localized topological boundary modes coexisting with a continuous spectrum of extended modes. They have been realized in systems with symmetry-protected topological phases, where their immunity to defects and perturbations depends on the presence of symmetries. Here we propose a method that transforms an in-gap topological boundary state into a BIC by using the concept of subsymmetry. We design the coupling between a system possessing in-gap topological modes and a system possessing a continuum of states that results in topological BICs. We define the criteria for the coupling that yields the desired results. To implement this scheme, we construct representative topological BICs based on one-dimensional Su-Schrieffer-Heeger models and implement them in photonic lattices. Our results not only reveal novel physical phenomena but may also provide methods for designing a new generation of topological devices.

Flat photonic surface bands pinned between Dirac points.

We point out that 2D photonic crystals (PhCs) can support surface bands that are pinned to Dirac points. These bands can be made very flat by optimizing the parameters of the system. Surface modes are found at the interface of two different cladding materials: one is a PhC with Dirac linear dispersion for the TE mode, and the other is a PhC that has a broad TE gap at the Dirac frequency.

Transverse electric plasmons in bilayer graphene.

We predict the existence of transverse electric (TE) plasmons in bilayer graphene. We find that their plasmonic properties are much more pronounced in bilayer than in monolayer graphene, in a sense that they can get more localized at frequencies just below hω = 0.4 eV for adequate doping values. This is a consequence of the perfectly nested bands in bilayer graphene which are separated by ∼ 0.4 eV.

Observation of random-phase lattice solitons.

The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or 'discrete') solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.

Nonlinear control of photonic higher-order topological bound states in the continuum.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

Nonlinear tuning of PT symmetry and non-Hermitian topological states.

Topology, parity-time (PT) symmetry, and nonlinearity are at the origin of many fundamental phenomena in complex systems across the natural sciences, but their mutual interplay remains unexplored. We established a nonlinear non-Hermitian topological platform for active tuning of PT symmetry and topological states. We found that the loss in a topological defect potential in a non-Hermitian photonic lattice can be tuned solely by nonlinearity, enabling the transition between PT-symmetric and non-PT-symmetric regimes and the maneuvering of topological zero modes. The interaction between two apparently antagonistic effects is revealed: the sensitivity close to exceptional points and the robustness of non-Hermitian topological states. Our scheme using single-channel control of global PT symmetry and topology via local nonlinearity may provide opportunities for unconventional light manipulation and device applications.

Universal momentum-to-real-space mapping of topological singularities.

Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned with a given pseudospin state s, we directly observe topological charge conversion that follows the rule l → l + 2s. Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams.

Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology.

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity, and what can happen to topological invariants during nonlinear propagation? To explore these questions, we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems. Performed on laser-written photonic Su-Schrieffer-Heeger lattices, our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection. Our theory explains all the observations well. Furthermore, we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology. These concepts are applicable to other nonlinear topological systems, both in higher dimensions and beyond our photonic platform.

Synthesis and observation of non-Abelian gauge fields in real space.

Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

Spontaneous pattern formation upon incoherent waves: from modulation-instability to steady-state.

We study the long-range propagation of incoherent light following the modulation instability (MI) process in non-instantaneous nonlinear Kerr-type media. We find that the system eventually reaches a steady-state characterized by a lower degree of coherence than in the initial state, with small fluctuations around a pronounced mean value. We find that the average values of the spatial correlation distance at steady-state and the fluctuations around it, which are obtained either through ensemble averaging, or by spatial averaging, or via temporal averaging, are all identical. This feature may be viewed as indication of ergodic behavior, which occurs in the long-time evolution following incoherent MI. Finally, we find that the steady-state properties of the system depend on the initial coherence but not on the nonlinearity strength, although the system evolves faster to steady-state as the strength of the nonlinearity is increased.

Incoherent modulation instability in a nonlinear photonic lattice.

We study modulation instability (MI) of random-phase waves in nonlinear photonic lattices. We find that an incoherent superposition of extended nonlinear eigenstates of the system, that is, an incoherent extended stationary beam, may become unstable due to nonlinearity. The instability process depends on the nonlinearity, on the structure of the diffraction curves of the lattice, as well as on the properties of the beam, whose spectrum can be comprised of Bloch modes from different bands, and from different regions of diffraction (normal/anomalous). This interplay among diffraction, incoherence, and nonlinearity leads to a variety of phenomena, including the possibility of tailoring the diffraction curve of the lattice, or the coherence properties of the beam, to enhance or suppress the instability. We present several examples of such phenomena, including a case where increasing the lattice depth flattens the diffraction curve thereby enhancing the instability, "locking" the most unstable mode to the edge of the 1st Brillouin zone for large nonlinearity, and incoherent MI in self-defocusing media.

Topologically enabled optical nanomotors.

Shaping the topology of light, by way of spin or orbital angular momentum engineering, is a powerful tool to manipulate matter on the nanoscale. Conventionally, such methods focus on shaping the incident beam of light and not the full interaction between the light and the object to be manipulated. We theoretically show that tailoring the topology of the phase space of the light particle interaction is a fundamentally more versatile approach, enabling dynamics that may not be achievable by shaping of the light alone. In this manner, we find that optically asymmetric (Janus) particles can become stable nanoscale motors even in a light field with zero angular momentum. These precessing steady states arise from topologically protected anticrossing behavior of the vortices of the optical torque vector field. Furthermore, by varying the wavelength of the incident light, we can control the number, orientations, and the stability of the spinning states. These results show that the combination of phase-space topology and particle asymmetry can provide a powerful degree of freedom in designing nanoparticles for optimal external manipulation in a range of nano-optomechanical applications.

Splashing transients of 2D plasmons launched by swift electrons.

Launching of plasmons by swift electrons has long been used in electron energy-loss spectroscopy (EELS) to investigate the plasmonic properties of ultrathin, or two-dimensional (2D), electron systems. However, the question of how a swift electron generates plasmons in space and time has never been answered. We address this issue by calculating and demonstrating the spatial-temporal dynamics of 2D plasmon generation in graphene. We predict a jet-like rise of excessive charge concentration that delays the generation of 2D plasmons in EELS, exhibiting an analog to the hydrodynamic Rayleigh jet in a splashing phenomenon before the launching of ripples. The photon radiation, analogous to the splashing sound, accompanies the plasmon emission and can be understood as being shaken off by the Rayleigh jet-like charge concentration. Considering this newly revealed process, we argue that previous estimates on the yields of graphene plasmons in EELS need to be reevaluated.

Incoherent solitons in instantaneous nonlocal nonlinear media.

We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave packets is played by the nonlocal (rather than the traditional noninstantaneous) nature of the nonlinearity. This kind of incoherent soliton has profoundly different features than other incoherent solitons.

Controlling Directionality and Dimensionality of Radiation by Perturbing Separable Bound States in the Continuum.

A bound state in the continuum (BIC) is an unusual localized state that is embedded in a continuum of extended states. Here, we present the general condition for BICs to arise from wave equation separability. Then we show that by exploiting perturbations of certain symmetry such BICs can be turned into resonances that radiate with a tailorable directionality and dimensionality. Using this general framework, we construct new examples of separable BICs and resonances that can exist in optical potentials for ultracold atoms, photonic systems, and systems described by tight binding. Such resonances with easily reconfigurable radiation allow for applications such as the storage and release of waves at a controllable rate and direction, as well systems that switch between different dimensions of confinement.

Efficient plasmonic emission by the quantum Cerenkov effect from hot carriers in graphene.

Graphene plasmons have been found to be an exciting plasmonic platform, thanks to their high field confinement and low phase velocity, motivating contemporary research to revisit established concepts in light-matter interaction. In a conceptual breakthrough over 80 years old, Cerenkov showed how charged particles emit shockwaves of light when moving faster than the phase velocity of light in a medium. To modern eyes, the Cerenkov effect offers a direct and ultrafast energy conversion scheme from charge particles to photons. The requirement for relativistic particles, however, makes Cerenkov emission inaccessible to most nanoscale electronic and photonic devices. Here we show that graphene plasmons provide the means to overcome this limitation through their low phase velocity and high field confinement. The interaction between the charge carriers flowing inside graphene and the plasmons enables a highly efficient two-dimensional Cerenkov emission, giving a versatile, tunable and ultrafast conversion mechanism from electrical signal to plasmonic excitation.

Gap random-phase lattice solitons.

We theoretically study gap random-phase lattice solitons (gap-RPLSs) in nonlinear waveguide arrays with self-defocusing nonlinearity. We find that the intensity structure and statistical (coherence) properties of gap-RPLSs conform to the lattice periodicity, while their Floquet-Bloch power spectrum is multi-humped with peaks in the anomalous diffractions regions. It is shown that a gap-RPLS can be generated when a simple incoherent beam with bell-shaped power spectrum and single-hump intensity is launched at a proper angle into the waveguide array. The input incoherent beam evolves in the lattice while shedding off some radiation, and eventually attains the features of gap-RPLS.