Manipulation of edge states in microwave artificial graphene

Edge states are one important ingredient to understand transport properties of graphene nanoribbons. We study experimentally the existence and the internal structure of edge states under uniaxial strain of the three main edges: zigzag, bearded, and armchair. The experiments are performed on artificial microwave graphene flakes, where the wavefunctions are obtained by direct imaging. We show that uniaxial strain can be used to manipulate the edge states: a single parameter controls their existence and their spatial extension into the ribbon. By combining tight-binding approach and topological arguments, we provide an accurate description of our experimental findings. A new type of zero-energy state appearing at the intersection of two edges, namely the corner state, is also observed and discussed.Comment: 15 pages, 9 figure

Tight-binding couplings in microwave artificial graphene

We experimentally study the propagation of microwaves in an artificial honeycomb lattice made of dielectric resonators. This evanescent propagation is well described by a tight-binding model, very much like the propagation of electrons in graphene. We measure the density of states, as well as the wave function associated with each eigenfrequency. By changing the distance between the resonators, it is possible to modulate the amplitude of next-(next-)nearest-neighbor hopping parameters and to study their effect on the density of states. The main effect is the density of states becoming dissymmetric and a shift of the energy of the Dirac points. We study the basic elements: An isolated resonator, a two-level system, and a square lattice. Our observations are in good agreement with analytical solutions for corresponding infinite lattice.Comment: 10 pages, 9 figure

Topological transition of Dirac points in a microwave experiment

By means of a microwave tight-binding analogue experiment of a graphene-like lattice, we observe a topological transition between a phase with a point-like band gap characteristic of massless Dirac fermions and a gapped phase. By applying a controlled anisotropy on the structure, we investigate the transition directly via density of states measurements. The wave function associated with each eigenvalue is mapped and reveals new states at the Dirac point, localized on the armchair edges. We find that with increasing anisotropy, these new states are more and more localized at the edges.Comment: Physical Review Letters (2013) XX

Observation of supersymmetric pseudo-Landau levels in strained microwave graphene

Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory. In particular, we resolve the full sublattice polarisation of the anomalous 0th pseudo-Landau level, which reveals a deep connection to zigzag edge states in the unstrained case

Partial chiral symmetry-breaking as a route to spectrally isolated topological defect states in two-dimensional artificial materials

Bipartite quantum systems from the chiral universality classes admit topologically protected zero modes at point defects. However, in two-dimensional systems these states can be difficult to separate from compacton-like localized states that arise from flat bands, formed if the two sublattices support a different number of sites within a unit cell. Here we identify a natural reduction of chiral symmetry, obtained by coupling sites on the majority sublattice, which gives rise to spectrally isolated point-defect states, topologically characterized as zero modes supported by the complementary minority sublattice. We observe these states in a microwave realization of a dimerized Lieb lattice with next-nearest neighbour coupling, and also demonstrate topological mode selection via sublattice-staggered absorption

Selective enhancement of topologically induced interface states

International audienceThe recent realization of topological phases in insulators and superconductors has raised the prospects to advance robust quantum technologies. The desire to demonstrate the underlying topological features with a high level of control has given incentive to explore optical platforms for analogous realizations. Here we show that the functionality of optical systems can be enhanced by combining topological protection with non-hermitian symmetries that do not have an electronic counterpart. This is achieved by combining parity-time symmetric losses with a unique feature of topologically induced interface states, namely, that they break a sublattice symmetry. This property isolates the state from the losses and enhances its visibility both in the frequency and in the time domain

Broadband integrated beam splitter using spatial adiabatic passage

Light routing and manipulation are important aspects of integrated optics. They essentially rely on beam splitters which are at the heart of interferometric setups and active routing. The most common implementations of beam splitters suffer either from strong dispersive response (directional couplers) or tight fabrication tolerances (multimode interference couplers). In this paper we fabricate a robust and simple broadband integrated beam splitter based on lithium niobate with a splitting ratio achromatic over more than 130 nm. Our architecture is based on spatial adiabatic passage, a technique originally used to transfer entirely an optical beam from a waveguide to another one that has been shown to be remarkably robust against fabrication imperfections and wavelength dispersion. Our device shows a splitting ratio of 0.52$\pm$0.03 and 0.48$\pm$0.03 from 1500\,nm up to 1630\,nm. Furthermore, we show that suitable design enables the splitting in output beams with relative phase 0 or $\pi$. Thanks to their independence to material dispersion, these devices represent simple, elementary components to create achromatic and versatile photonic circuits