Classical diffusive dynamics for the quasiperiodic kicked rotor

We study the classical dynamics of a quasiperiodic kicked rotor, whose quantum counterpart is known to be an equivalent of the 3D Anderson model. Using this correspondence allowed for a recent experimental observation of the Anderson transition with atomic matter waves. In such a context, it is particularly important to assert the chaotic character of the classical dynamics of this system. We show here that it is a 3D anisotropic diffusion. Our simple analytical predictions for the associated diffusion tensor are found in good agreement with the results of numerical simulations.Comment: 8 pages, 7 figures, submitted to Jour. Mod. Opt

Quantum scaling laws in the onset of dynamical delocalization

We study the destruction of dynamical localization, experimentally observed in an atomic realization of the kicked rotor, by a deterministic Hamiltonian perturbation, with a temporal periodicity incommensurate with the principal driving. We show that the destruction is gradual, with well defined scaling laws for the various classical and quantum parameters, in sharp contrast with predictions based on the analogy with Anderson localization.Comment: 3 pages, revtex

Quantifying topological protection in valley photonic crystals using triangular resonators

The realization of photonic crystal waveguides with topological protection enables robust light propagation against defect-induced scattering. It should allow the design of very compact devices by exploiting guiding through sharp bends with low losses and back-reflection. In this work, we use valley-topological triangular resonators coupled to an input waveguide to evaluate the quality of the topological protection. To that purpose, we analyze via numerical simulations the existence of backward scattering at cavity corners or transmission with pseudo-spin conversion at the splitter between the input waveguide and the cavity. We evidence that a breakdown of topological protection takes place, in particular at sharp corners, which results in transmission minima and split-resonances, otherwise non-existent. In order to evaluate the small coupling coefficients associated to this breakdown, a phenomenological model based on an ad hoc parameterization of scattering matrices at splitters and corners of the resonators is introduced. By comparison with the numerical simulations, we are able to quantify the loss of topological protection at sharp bends and splitters. Finally, varying the coupling rate between the input waveguide and the cavity by introducing a small gap allows reaching quality factors on the order of 10^4 to 10^6 . Our results suggest that even in a perfectly ordered system, topological protection is not complete at corners, sharp bends and splitters, which is crucial to design photonic devices which gather compactness and low losses through topological conduction of electromagnetic waves.Comment: 23 pages, 7 figures, one supplementary informations fil

Controlling symmetry and localization with an artificial gauge field in a disordered quantum system

Anderson localization, the absence of diffusion in disordered media, draws its origins from the destructive interference between multiple scattering paths. The localization properties of disordered systems are expected to be dramatically sensitive to their symmetry characteristics. So far however, this question has been little explored experimentally. Here, we investigate the realization of an artificial gauge field in a synthetic (temporal) dimension of a disordered, periodically-driven (Floquet) quantum system. Tuning the strength of this gauge field allows us to control the time-reversal symmetry properties of the system, which we probe through the experimental observation of three symmetry-sensitive `smoking-gun' signatures of localization. The first two are the coherent backscattering, marker of weak localization, and the coherent forward scattering, genuine interferential signature of Anderson localization, observed here for the first time. The third is the direct measurement of the $\beta(g)$ scaling function in two different symmetry classes, allowing to demonstrate its universality and the one-parameter scaling hypothesis