Two-Dimensional Topological Polariton Laser

Topological valley Hall polariton condensation

A photonic topological insulator features robust directional propagation and immunity to defect perturbations of the edge/surface state. Exciton-polaritons, that is, the hybrid quasiparticles of excitons and photons in semiconductor microcavities, have been proposed as a tunable nonlinear platform for emulating topological phenomena. However, mainly due to excitonic material limitations, experimental observations so far have not been able to enter the nonlinear condensation regime or only show localized condensation in one dimension. Here we show a topological propagating edge state with polariton condensation at room temperature and without any external magnetic field. We overcome material limitations by using excitonic CsPbCl3 halide perovskites with a valley Hall lattice design. The polariton lattice features a large bandgap of 18.8 meV and exhibits strong nonlinear polariton condensation with clear long-range spatial coherence across the critical pumping density. The geometric parameters and material composition of our nonlinear many-body photonic system platform can in principle be tailored to study topological phenomena of other interquasiparticle interactions.

Photonic Bound States in the Continuum in Nanostructures

Bound states in the continuum (BIC) have garnered considerable attention recently for their unique capacity to confine electromagnetic waves within an open or non-Hermitian system. Utilizing a variety of light confinement mechanisms, nanostructures can achieve ultra-high quality factors and intense field localization with BIC, offering advantages such as long-living resonance modes, adaptable light control, and enhanced light-matter interactions, paving the way for innovative developments in photonics. This review outlines novel functionality and performance enhancements by synergizing optical BIC with diverse nanostructures, delivering an in-depth analysis of BIC designs in gratings, photonic crystals, waveguides, and metasurfaces. Additionally, we showcase the latest advancements of BIC in 2D material platforms and suggest potential trajectories for future research.

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.

Photonic Dirac cavities with spatially varying mass term

In recent years, photonics has proven itself as an excellent platform for emulation of relativistic phenomena. Here, we show an example of relativistic-like trapping in photonic system that realizes Dirac-like dispersion with spatially inhomogeneous mass term. The modes trapped by such cavities, their energy levels, and corresponding orbitals are then characterized through optical imaging in real and momentum space. The fabricated cavities host a hierarchy of photonic modes with distinct radiation profiles directly analogous to various atomic orbitals endowed with unique characteristics, such as pseudo-particle-hall symmetry and spin degeneracy, and they carry topological charge which gives rise to radiative profiles with angular momentum. We demonstrate that these modes can be directionally excited by pseudo-spin-polarized boundary states. In addition to the fundamental interest in the structure of these pseudo-relativistic orbitals, the proposed system offers a route for designing new types of nanophotonic devices, spin-full resonators and topological light sources compatible with integrated photonics platforms.

Triangular bright solitons in nonlinear optics and Bose-Einstein condensates

We demonstrate what we believe to be novel triangular bright solitons that can be supported by the nonlinear Schrödinger equation with inhomogeneous Kerr-like nonlinearity and external harmonic potential, which can be realized in nonlinear optics and Bose-Einstein condensates. The profiles of these solitons are quite different from the common Gaussian or sech envelope beams, as their tops and bottoms are similar to the triangle and inverted triangle functions, respectively. The self-defocusing nonlinearity gives rise to the triangle-up solitons, while the self-focusing nonlinearity supports the triangle-down solitons. Here, we restrict our attention only to the lowest-order fundamental triangular solitons. All such solitons are stable, which is demonstrated by the linear stability analysis and also clarified by direct numerical simulations. In addition, the modulated propagation of both types of triangular solitons, with the modulated parameter being the strength of nonlinearity, is also presented. We find that such propagation is strongly affected by the form of the modulation of the nonlinearity. For example, the sudden change of the modulated parameter causes instabilities in the solitons, whereas the gradual variation generates stable solitons. Also, a periodic variation of the parameter causes the regular oscillation of solitons, with the same period. Interestingly, the triangle-up and triangle-down solitons can change into each other, when the parameter changes the sign.

Experimental realization of a reconfigurable Lieb photonic lattice in a coherent atomic medium

We have experimentally demonstrated the realization of an instantaneously reconfigurable Lieb photonic lattice with a flatband in a three-level Λ-type rubidium atomic configuration. Such a coherently controllable Lieb photonic lattice is optically induced by a coupling field possessing a spatially periodic intensity distribution (generated via a spatial light modulator) under the condition of electromagnetically induced transparency. The incident weak Gaussian probe field can experience discrete diffraction and the observed probe beam at the output surface of the medium exhibits the same Lieb pattern, verifying the formation of the refractive index with a Lieb profile inside the atomic vapor cell. The potential wells and the band structure of the Lieb photonic lattice can be effectively manipulated by easily tuning the frequency of the involved laser beams. The current work can promisingly pave the way for exploring the exotic dynamics as well as tunable photonic devices in Lieb photonic lattices.

Topological laser with higher-order corner states in the 2-dimensional Su-Schrieffer-Heeger model

A nonlinear non-Hermitian topological laser system based on the higher-order corner states of the 2-dimensional (2D) Su-Schrieffer-Heeger (SSH) model is investigated. The topological property of this nonlinear non-Hermitian system described by the quench dynamics is in accordance with that of a normal 2D SSH model. In the topological phase, all sites belonging to the topological corner states begin to emit stable laser light when a pulse is given to any one site of the lattice, while no laser light is emitted when the lattice is in the trivial phase. Furthermore, the next-nearest-neighbor (NNN) couplings are introduced into the strong-coupling unit cells of the 2D SSH model, which open a band gap in the continuous band structure. In the topological phase, similar to the case of 2D SSH model without NNN couplings, the corner sites can emit stable laser light due to the robustness of the higher-order corner states when the NNN couplings are regarded as the perturbation. However, amplitude of the stimulated site does not decay to zero in the trivial phase, because the existence of the NNN couplings in the strong-coupling unit cells make the lattice like one in the tetramer limit, and a weaker laser light is emitted by each corner.

Programmable Polariton Topological Insulators All-Optically Controlled by the Stark Effect

Efficiently and flexibly manipulating unidirectional edge states is key to developing topological insulators as functional devices. In this work, we propose an all-optical method that utilizes the valley-selective optical Stark effect to realize programmable topological insulators. We pattern a two-dimensional honeycomb structure in an exciton-polariton platform resulting from a strong light-matter coupling in a monolayer transition metal dichalcogenide. The optical Stark effect is induced to generate a pseudo magnetic field, combined with spin-orbit coupling to form the topological one-way edge states of the polariton. On account of the ultrafast switching speed and precisely spatial controllability of the optical Stark effect, two applications, i.e., ports ratio tunable polariton splitter and programmable polariton router, were demonstrated, showing designable and rewritable functionality of all-optically controllable polariton topological insulators. This study paves the way to robustly and intelligently control/form polaritonic and spintronic devices for future classical and quantum information processing and application.

Germanium Monosulfide as a Natural Platform for Highly Anisotropic THz Polaritons

Terahertz (THz) electromagnetic radiation is key to access collective excitations such as magnons (spins), plasmons (electrons), or phonons (atomic vibrations), thus bridging topics between optics and solid-state physics. Confinement of THz light to the nanometer length scale is desirable for local probing of such excitations in low-dimensional systems, thereby circumventing the large footprint and inherently low spectral power density of far-field THz radiation. For that purpose, phonon polaritons (PhPs) in anisotropic van der Waals (vdW) materials have recently emerged as a promising platform for THz nanooptics. Hence, there is a demand for the exploration of materials that feature not only THz PhPs at different spectral regimes but also host anisotropic (directional) electrical, thermoelectric, and vibronic properties. To that end, we introduce here the semiconducting vdW-material alpha-germanium(II) sulfide (GeS) as an intriguing candidate. By employing THz nanospectroscopy supported by theoretical analysis, we provide a thorough characterization of the different in-plane hyperbolic and elliptical PhP modes in GeS. We find not only PhPs with long lifetimes (τ > 2 ps) and excellent THz light confinement (λ0/λ > 45) but also an intrinsic, phonon-induced anomalous dispersion as well as signatures of naturally occurring, substrate-mediated PhP canalization within a single GeS slab.

Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer

Chiral edge states are highly sought after as paradigmatic topological states relevant to both quantum information processing and dissipationless electron transport. Using superconducting transmon-based quantum computers, we demonstrate chiral topological propagation that is induced by suitably designed interactions, instead of flux or spin-orbit coupling. Also different from conventional 2D realizations, our effective Chern lattice is implemented on a much smaller equivalent 1D spin chain, with sequences of entangling gates encapsulating the required time-reversal breaking. By taking advantage of the quantum nature of the platform, we circumvented difficulties from the limited qubit number and gate fidelity in present-day noisy intermediate-scale quantum era quantum computers, paving the way for the quantum simulation of more sophisticated topological states on very rapidly developing quantum hardware.

Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.

Valley Hall edge solitons in a photonic graphene

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Dual measurements of temporal and spatial coherence of light in a single experimental setup using a modified Michelson interferometer

An experimental technique is developed to simultaneously measure both temporal and spatial coherences of a light source by altering a standard Michelson interferometer, which has been primarily used for measuring temporal coherence only. Instead of using simple plane mirrors, two retroreflectors and their longitudinal and lateral movements are utilized to incorporate spatial coherence measurement using this modified Michelson interferometer. In general, one uses Young's double slit interferometer to measure spatial coherence. However, this modified interferometer can be used as an optical setup kept at room temperature outside a cryostat to measure the spatiotemporal coherence of a light source placed at cryogenic temperatures. This avoids the added complexities of modulation of interference fringe patterns due to single slit diffraction as well. The process of mixing of spatial and temporal parts of coherences is intrinsic to existing methods for dual measurements. We addressed these issues of spatiotemporal mixing, and we introduced a method of "temporal filtering" in spatial coherence measurements. We also developed a "curve overlap" method that is used to extend the range of the experimental setup during temporal coherence measurements without compromising the precision. Together, these methods provide major advantages over plane mirror based standard interferometric systems for dual measurements in avoiding systematic errors, which lead to inaccuracies, especially for light sources with low coherences.

Topological solitons in arrays of modelocked lasers

We report spatiotemporal topological solitons in an array of modelocked lasers. In its conservative limit, our model reduces to the famous Su-Schrieffer-Heeger system possessing topological states inside the gap of its linear spectrum. We report one-dimensional spatial and two-dimensional spatiotemporal topological solitons, i.e., bullets, with the operational frequencies locked to the values inside the topological gap.

Coherent transfer of topological interface states

We demonstrate the controlled coherent transfer of topological interface states in a one-dimensional non-Hermitian chain of interacting Bose-Einstein condensates. The topological protection stems from a spatially patterned pump in an open-dissipative system. As a test bed setup of the proposed phenomenon, we consider a chain of coupled micropillars with embedded quantum wells, possessing exciton-polariton resonances. The transfer of an interface state is driven by spatially localised, adiabatic pump modulation in the vicinity of the interface state. The stochastic calculations prove the coherent nature of the interface state transfer. For appropriate system parameters the coherence degree is preserved after multiple transitions, paving the way towards long-range transfer of a coherent quantum state.

Chiral condensates in a polariton hexagonal ring

We model the generation of vortex modes in exciton-polariton condensates in semiconductor micropillars, arranged into a hexagonal ring molecule, in the presence of TE-TM splitting. This splitting lifts the degeneracy of azimuthally modulated vortex modes with opposite topological charges supported by this structure, so that a number of non-degenerate vortex states characterized by different combinations of topological charges in two polarization components appears. We present a full bifurcation picture for such vortex modes and show that because they have different energies they can be selectively excited by coherent pump beams with specific frequencies and spatial configurations. At high pumping intensity, polariton-polariton interactions give rise to the coupling of different vortex resonances and a bistable regime is achieved.

Nonlinear higher-order polariton topological insulator

We address the resonant response and bistability of the exciton-polariton corner states in a higher-order nonlinear topological insulator realized with a kagome arrangement of microcavity pillars. Such states are resonantly excited and exist due to the balance between pump and losses, on one hand, and between nonlinearity and dispersion in inhomogeneous potential landscape, on the other hand, for pump energy around eigen-energies of corresponding linear localized modes. Localization of the nonlinear corner states in a higher-order topological insulator can be efficiently controlled by tuning pump energy. We link the mechanism of corner state formation with symmetry of the truncated kagome array. Corner states coexist with densely packed edge states but are well isolated from them in energy. Nonlinear corner states persist even in the presence of perturbations in a corner microcavity pillar.

PT-Symmetric Topological Edge-Gain Effect

We demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped subsystems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants (w0,wπ)∈2Z×2Z. Under the open boundary condition, these invariants further predict the number of zero- and π-quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

Observation of edge solitons in photonic graphene

Edge states emerge in diverse areas of science, offering promising opportunities for the development of future electronic or optoelectronic devices, sound and light propagation control in acoustics and photonics. Previous experiments on edge states in photonics were carried out mostly in linear regimes, but the current belief is that nonlinearity introduces more striking features into physics of edge states, leading to the formation of edge solitons, optical isolation, making possible stable lasing in such states, to name a few. Here we report the observation of edge solitons at the zigzag edge of a reconfigurable photonic graphene lattice created via the effect of electromagnetically induced transparency in an atomic vapor cell with controllable nonlinearity. To obtain edge solitons, Raman gain is introduced to compensate strong absorption experienced by the edge state during propagation. Our observations may open the way for future experimental exploration of topological photonics on this nonlinear, reconfigurable platform.