Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.Comment: 10 pages, 7 color figures (incl. appendices) Close to the published versio

Red light-emitting Carborane-BODIPY dyes: Synthesis and properties of visible-light tuned fluorophores with enhanced boron content

A small library of 2,6- and 3,5-distyrenyl-substituted carborane-BODIPY dyes was efficiently synthesized by means of a Pd-catalyzed Heck coupling reaction. Styrenyl-carborane derivatives were exploited as molecular tools to insert two carborane clusters into the fluorophore core and to extend the π-conjugation of the final molecule in a single synthetic step. The synthetic approach allows to increase the molecular diversity of this class of fluorescent dyes by the synthesis of symmetric or asymmetric units with enhanced boron content. The structural characterization and the photoluminescence (PL) properties of synthesized dyes were evaluated, and the structure/properties relationships have been investigated by theoretical calculations. The developed compounds exhibit a significant bathochromic shift compared to their parent fluorophore scaffolds, and absorption and emission patterns were practically unaffected by the different substituents (Me or Ph) on the Ccluster atom (Cc) of the carborane cage or the cluster isomer (ortho- or meta-carborane). Remarkably, the presence of carborane units at 2,6-positions of the fluorophore produced a significant increase of the emission fluorescent quantum yields, which could be slightly tuned by changing the Cc-substituent and the carborane isomer, as well as introducing ethylene glycol groups at the meso-position of the BODIPY

Distilling the topology of the Hofstadter model through a diffraction experiment

In two and three spatial dimensions, the transverse response experienced by a charged particle on a lattice in a uniform magnetic field is proportional to a topological invariant, the first Chern number, characterizing the energy bands of the underlying Hofstadter Hamiltonian. In four dimensions, the transverse response is also quantized, and controlled by the second Chern number. These remarkable features solely arise from the magnetic translational symmetry. Here we show that the symmetries of the two-, three- and four-dimensional Hofstadter Hamiltonians may be encrypted in optical diffraction gratings, such that simple photonic experiments allow one to extract the first and the second Chern numbers of the whole energy spectra. This result is particularly remarkable in three and four dimensions, where complete topological characterizations have not yet been achieved experimentally. Side-by-side to the theoretical analysis, in this work we present the experimental study of optical gratings analogues of the two- and three-dimensional Hofstadter models