Universal Sign Control of Coupling in Tight-Binding Lattices

Realization of Gapped and Ungapped Photonic Topological Anderson Insulators

It is commonly believed that topologically nontrivial one-dimensional systems support edge states rather than bulk states at zero energy. In this work, we find an unanticipated case of topological Anderson insulator (TAI) phase where two bulk modes are degenerate at zero energy, in addition to degenerate edge modes. We term this "ungapped TAI" to distinguish it from the previously known gapped TAIs. Our experimental realization of both gapped and ungapped TAIs relies on coupled photonic resonators, in which the disorder in coupling is judiciously engineered by adjusting the spacing between the resonators. By measuring the local density of states both in the bulk and at the edges, we demonstrate the existence of these two types of TAIs, together forming a TAI plateau in the phase diagram. Our experimental findings are well supported by theoretical analysis. In the ungapped TAI phase, we observe stable coexistence of topological edge states and localized bulk states at zero energy, highlighting the distinction between TAIs and traditional topological insulators.

Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.

Projectively Enriched Symmetry and Topology in Acoustic Crystals

Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a Z_{2} gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator, and graphenelike semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology and opens the door to a vast unexplored land of topological states by projective symmetries.

Geometric control of next-nearest-neighbor coupling in evanescently coupled dielectric waveguides

We experimentally demonstrate that the next-nearest-neighbor-coupling (NNN-coupling) in an array of waveguides can naturally be negative. To do so, dielectric zig-zag shaped waveguide arrays are fabricated with direct laser writing (DLW). By changing the angle of the zig-zag shape it is possible to tune between positive and negative ratios of nearest and next-nearest-neighbor coupling, which also allows to reduce the impact of the NNN-coupling to zero at the correct respective angle. We confirm the existence of negative NNN-couplings experimentally and show the improved accuracy of a refined tight-binding model. Our results are also of importance for other discrete systems in which the tight-binding model is often used.

Gauge-Field Extended k·p Method and Novel Topological Phases

Although topological artificial systems, like acoustic and photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable Z_{2} gauge fields. Hence, it is fundamentally important to explore new topological phases based on these features. Here, we point out that the Z_{2} gauge field leads to two fundamental modifications of the conventional k·p method: (i) The little co-group must include the translations with nontrivial algebraic relations. (ii) The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular π-flux model exhibiting graphenelike semimetal phases, and a graphite model with interlayer π flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to crystalline systems with gauge fields and establishes the approach to analyze these phases.

Exploring complex graphs using three-dimensional quantum walks of correlated photons

Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in quantum communication and quantum search algorithms in highly branched quantum networks. Here, we introduce a previously unidentified paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks by exploiting the hybrid action of spatial and polarization degrees of freedom of photon pairs in complex waveguide circuits with tailored birefringence. This testbed for the experimental exploration of multiparticle quantum walks on complex, highly connected graphs paves the way toward exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.

Acoustic Realization of Quadrupole Topological Insulators

A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here, we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge, and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping.

Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings

We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

Observation of an acoustic octupole topological insulator

Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.

A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages

Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized nonlocal property commonly manifests through exotic bulk phenomena and corresponding robust boundary effects. In our work we study a system where the spectral bands are associated with non-quantized indices, but nevertheless possess robust boundary states. We present a theoretical analysis, where we show that the square of the Hamiltonian exhibits quantized indices. The findings are experimentally demonstrated by using photonic Aharonov-Bohm cages.

Coupling between Exciton-Polariton Corner Modes through Edge States

Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional localized corner modes that reside within the band gap of the system along with edge modes that inhabit a band edge next to bulk modes. Thanks to the topological nature, information can be trapped at the corners of these systems, which will be unhampered even in the presence of disorder. Being localized at the corners, the exchange of information among the corner states is an issue. Here we show that the nonlinearity in an exciton polariton system can allow the coupling between the different corners through the edge states based on optical parametric scattering, realizing a system of multiple connectible topological modes.

Quantum Network Transfer and Storage with Compact Localized States Induced by Local Symmetries

We propose modulation protocols designed to generate, store, and transfer compact localized states in a quantum network. Induced by parameter tuning or local reflection symmetries, such states vanish outside selected domains of the complete system and are therefore ideal for information storage. Their creation and transfer is here achieved either via amplitude phase flips or via optimal temporal control of intersite couplings. We apply the concept to a decorated, locally symmetric Lieb lattice where one sublattice is dimerized, and also demonstrate it for more complex setups. The approach allows for a flexible storage and transfer of states along independent paths in lattices supporting flat energetic bands. We further demonstrate a method to equip any network featuring static perfect state transfer of single-site excitations with compact localized states, thus increasing the storage ability of these networks. We show that these compact localized states can likewise be perfectly transferred through the corresponding network by suitable, time-dependent modifications. The generic network and protocols proposed can be utilized in various physical setups such as atomic or molecular spin lattices, photonic waveguide arrays, and acoustic setups.

Topological bound modes in anti-PT-symmetric optical waveguide arrays

We investigate the topological bound modes in a binary optical waveguide array with anti-parity-time (PT) symmetry. The anti-PT-symmetric arrays are realized by incorporating additional waveguides to the bare arrays, such that the effective coupling coefficients are imaginary. The systems experience two kinds of phase transition, including global topological order transition and quantum phase transition. As a result, the system supports two kinds of robust bound modes, which are protected by the global topological order and the quantum phase, respectively. The study provides a promising approach to realizing robust light transport by utilizing mediating components.

Parity anomaly laser

We propose a novel supersymmetry-inspired scheme for achieving robust single-mode lasing in arrays of coupled microcavities, based on factorizing a given array Hamiltonian into its "supercharge" partner array. Pumping a single sublattice of the partner array preferentially induces lasing of an unpaired zero mode. A chiral symmetry protects the zero mode similar to 1D topological arrays, but it need not be localized to domain walls or edges. We demonstrate single-mode lasing over a wider parameter regime by designing the zero mode to have a uniform intensity profile.

Spoof Plasmonics: From Metamaterial Concept to Topological Description

Advances in metamaterials have offered the opportunity of engineering electromagnetic properties beyond the limits of natural materials. A typical example is "spoof" surface plasmon polaritons (SPPs), which mimic features of SPPs without penetrating into metal, but only with periodic corrugations on metal surfaces. They hold considerable promise in device applications from microwaves to the far infrared, where real SPP modes do not exist. The original spoof SPP concept is derived from the description of corrugated surfaces by a metamaterial that hosts an effective plasma frequency. Later, studies have attempted to describe spoof SPP modes with the band structure by strictly solving Maxwell's equations, which can possess band gaps from polaritonic anticrossing principle or Bragg interference. More recently, as inspired by the development of topological framework in condensed matter physics, the topological description of spoof SPPs is used to propose topologically protected waveguiding phenomena. Here, the developments of spoof SPPs from both practical and fundamental perspectives are reviewed.

Quantized electric multipole insulators

The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.

Forward/Backward Switching of Plasmonic Wave Propagation Using Sign-Reversal Coupling

Backward waves with wave-front propagation opposite in direction to that of energy flow have attracted considerable interest in the context of photonic metamaterials. However, switching between forward and backward waves in the same frequency range has remained a challenge. Here, on a platform of coupled designer surface plasmon resonators in the microwave regime, multiband forward/backward switching of plasmonic wave propagation is demonstrated. This approach makes use of sign-reversal coupling that occurs when switching the coupling configuration between tightly confined photonic modes. Direct experimental measurements of plasmon dispersion curves confirm the forward/backward propagation of plasmonic waves in the same frequency range. This study provides a solution to forward/backward switching of subwavelength plasmonic wave propagation, and may find potential applications in photonic integrated systems.

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.