Limits of topological protection under local periodic driving

Generation of higher-order topological insulators using periodic driving

Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.

Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

We study the disconnected entanglement entropy (DEE) of a Kitaev chain in which the chemical potential is periodically modulated withδ-function pulses within the framework of Floquet theory. For this driving protocol, the DEE of a sufficiently large system with open boundary conditions turns out to be integer-quantized, with the integer being equal to the number of Majorana edge modes localized at each edge of the chain generated by the periodic driving, thereby establishing the DEE as a marker for detecting Floquet Majorana edge modes. Analyzing the DEE, we further show that these Majorana edge modes are robust against weak spatial disorder and temporal noise. Interestingly, we find that the DEE may, in some cases, also detect the anomalous edge modes which can be generated by periodic driving of the nearest-neighbor hopping, even though such modes have no topological significance and not robust against spatial disorder. We also probe the behavior of the DEE for a kicked Ising chain in the presence of an integrability breaking interaction which has been experimentally realized.

Photonic quadrupole topological insulator using orbital-induced synthetic flux

The rich physical properties of multiatomic crystals are determined, to a significant extent, by the underlying geometry and connectivity of atomic orbitals. The mixing of orbitals with distinct parity representations, such as s and p orbitals, has been shown to be useful for generating systems that require alternating phase patterns, as with the sign of couplings within a lattice. Here we show that by breaking the symmetries of such mixed-orbital lattices, it is possible to generate synthetic magnetic flux threading the lattice. We use this insight to experimentally demonstrate quadrupole topological insulators in two-dimensional photonic lattices, leveraging both s and p orbital-type modes. We confirm the nontrivial quadrupole topology by observing the presence of protected zero-dimensional states, which are spatially confined to the corners, and by confirming that these states sit at mid-gap. Our approach is also applicable to a broader range of time-reversal-invariant synthetic materials that do not allow for tailored connectivity, and in which synthetic fluxes are essential.

Bound states in the continuum in waveguide arrays within a symmetry classification scheme

We study a photonic implementation of a modified Fano-Anderson model - a waveguide array with two additional waveguides and by using the coupled mode theory we calculate its spectral and scattering properties. We classify eigenmodes according to vertical symmetry of the structure given by self-coupling coefficients of the additional waveguides and establish the conditions for bound states in the continuum (BIC) existence. The main predictions drawn from the theoretical model are verified by rigorous full-wave simulations of realistic structures. We use the Weierstrass factorization theorem and interpret the scattering spectra of the systems with broken symmetry in terms of the eigenmodes. The Fano resonance related with excitation of quasi-BIC is explained as arising from the interference between this mode and another leaky mode.

Generalized laws of refraction and reflection at interfaces between different photonic artificial gauge fields

Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed a growing interest in artificial gauge fields generated either by the geometry or by time-dependent modulation, as they have been enablers of topological phenomena and synthetic dimensions in many physical settings, e.g., photonics, cold atoms, and acoustic waves. Here, we formulate and experimentally demonstrate the generalized laws of refraction and reflection at an interface between two regions with different artificial gauge fields. We use the symmetries in the system to obtain the generalized Snell law for such a gauge interface and solve for reflection and transmission. We identify total internal reflection (TIR) and complete transmission and demonstrate the concept in experiments. In addition, we calculate the artificial magnetic flux at the interface of two regions with different artificial gauge fields and present a method to concatenate several gauge interfaces. As an example, we propose a scheme to make a gauge imaging system-a device that can reconstruct (image) the shape of an arbitrary wavepacket launched from a certain position to a predesigned location.

Observation of topological transport quantization by dissipation in fast Thouless pumps

Quantized dynamics is essential for natural processes and technological applications alike. The work of Thouless on quantized particle transport in slowly varying potentials (Thouless pumping) has played a key role in understanding that such quantization may be caused not only by discrete eigenvalues of a quantum system, but also by invariants associated with the nontrivial topology of the Hamiltonian parameter space. Since its discovery, quantized Thouless pumping has been believed to be restricted to the limit of slow driving, a fundamental obstacle for experimental applications. Here, we introduce non-Hermitian Floquet engineering as a new concept to overcome this problem. We predict that a topological band structure and associated quantized transport can be restored at driving frequencies as large as the system's band gap. The underlying mechanism is suppression of non-adiabatic transitions by tailored, time-periodic dissipation. We confirm the theoretical predictions by experiments on topological transport quantization in plasmonic waveguide arrays.

Transport signatures of symmetry protection in 1D Floquet topological insulators

Time-periodic external drives have emerged as a powerful tool to artificially create topological phases of matter. Prime examples are Floquet topological insulators (FTIs), where a gapped bulk supports in-gap edge states, protected against symmetry-preserving local perturbations. Similar to an ordinary static topological insulator, the robustness of an edge state in a one-dimensional (1D) FTI shows up as a pinning of its quasienergy level, but now inside one of two distinct bulk gaps. Here we propose a scheme for probing this unique feature by observing transport characteristics of a 1D finite-sized FTI attached to external leads. We present predictions for transmission spectra using a nonequilibrium Green's function approach. Our analysis covers FTIs with time-independent and periodically driven boundary perturbations which either preserve or break the protecting chiral symmetry.