Abstract:Edge modes in topological insulators are known to be robust against defects. We investigate if this also holds true when the defect is not static, but varies in time. We study the influence of defects with timedependent coupling on the robustness of the transport along the edge in a Floquet system of helically curved waveguides. Waveguide arrays are fabricated via direct laser writing in a negative tone photoresist. We find that single dynamic defects do not destroy the chiral edge current, even when the tempo… Show more
“…Therefore, these examples pose no threat to the robustness of topological phases against local perturbations, since these are global in nature and, quite trivially, do not require gapclosing for a topological transition to occur. There have also been many works studying the properties of topological insulators and their robustness against local perturbations and disorder [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”
Finite topologically non-trivial systems are characterised, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in-gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulkedge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown in [Phys. Rev. Lett. 71, 3697 (1993)] and [Phys. Rev. A 89, 023619 (2014)]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of non-topological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localised impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.
“…Therefore, these examples pose no threat to the robustness of topological phases against local perturbations, since these are global in nature and, quite trivially, do not require gapclosing for a topological transition to occur. There have also been many works studying the properties of topological insulators and their robustness against local perturbations and disorder [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”
Finite topologically non-trivial systems are characterised, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in-gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulkedge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown in [Phys. Rev. Lett. 71, 3697 (1993)] and [Phys. Rev. A 89, 023619 (2014)]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of non-topological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localised impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.
“…All topological properties are lost in the long time limit as the system evolves towards a uniform, featureless steady state. The problem of decoherence due to driving noise has been recognized both theoretically and experimentally, starting from early measurements of the quantum kicked rotor in the 90s [89,90], and an active research field has emerged from studying and attempting to mitigate this effect [26,27,[91][92][93][94][95][96][97][98][99][100][101][102][103][104]. In our work, we have found a way of eliminating this effect completely: driving noise cannot lead to decoherence if unitary topological phases are realized without any driving.…”
We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators.
We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup.
We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator.
To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices.
Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving.
As benefit, the topological system does not suffer from decoherence and heating.
“…7b, c, respectively. The sample fabrication included two steps 26 . First, the inverse of the waveguide structure was 3D-printed by two-photon lithography in a negative-tone photoresist (IP-Dip, Nanoscribe).…”
Section: Methodsmentioning
confidence: 99%
“…We analyse such perturbations in the Su-Schriefer-Heeger (SSH) model, a simple yet topologically non-trivial system. The unique combination of two independent experimental quantum simulators allows for precise control of the system’s parameters as well as an uncomplicated detection technique 22–26 .Fig. 1Sketches of the SSH chains with time-periodic perturbations of a single lattice site at the interface between two distinct dimerisations (top) and the corresponding experimental realisations (bottom). a In-plane modulation of the boundary implemented in a plasmonic waveguide array.…”
The bulk-edge correspondence guarantees that the interface between two topologically distinct insulators supports at least one topological edge state that is robust against static perturbations. Here, we address the question of how dynamic perturbations of the interface affect the robustness of edge states. We illuminate the limits of topological protection for Floquet systems in the special case of a static bulk. We use two independent dynamic quantum simulators based on coupled plasmonic and dielectric photonic waveguides to implement the topological Su-Schriefer-Heeger model with convenient control of the full space- and time-dependence of the Hamiltonian. Local time-periodic driving of the interface does not change the topological character of the system but nonetheless leads to dramatic changes of the edge state, which becomes rapidly depopulated in a certain frequency window. A theoretical Floquet analysis shows that the coupling of Floquet replicas to the bulk bands is responsible for this effect. Additionally, we determine the depopulation rate of the edge state and compare it to numerical simulations.
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