Search

Symmetry reduced three-disk and five-disk systems are studied in a microwave setup. Using harmonic inversion the distribution of the imaginary parts of the resonances is determined. With increasing opening of the systems, a spectral gap is observed for thick as well as for thin repellers and for the latter case it is compared with the known topological pressure bounds. The maxima of the distributions are found to coincide for a large range of the distance to radius parameter with half of the classical escape rate. This confirms theoretical predictions based on rigorous mathematical analysis for the spectral gap and on numerical experiments for the maxima of the distributions. [ABSTRACT FROM AUTHOR]

Nonlinearity-induced asymmetric transport (AT) can be utilized for on-chip implementation of nonreciprocal devices that do not require odd-vector biasing. This scheme, however, is subject to a fundamental bound dictating that the maximum transmittance asymmetry is inversely proportional to the asymmetry intensity range (AIR) over which AT occurs. Contrary to the conventional wisdom, we show that the implementation of losses can lead to an increase of the AIR without deteriorating the AT. We develop a general theory that provides a new upper bound for AT in nonlinear complex systems and highlights the importance of their structural complexity and of losses. Our predictions are confirmed numerically and experimentally using a microwave complex network of coaxial cables.

We present wave transport experiments in hyperuniform disordered arrays of cylinders with high dielectric permittivity. Using microwaves, we show that the same material can display transparency, photon diffusion, Anderson localization, or a full band gap, depending on the frequency ν of the electromagnetic wave. Interestingly, we find a second weaker band gap, which appears to be related to the second peak of the structure factor. Our results emphasize the importance of spatial correlations on different length scales for the formation of photonic band gaps.

We investigate, using a microwave platform consisting of a non-Hermitian Su-Schrieffer-Heeger array of coupled dielectric resonators, the interplay of a lossy nonlinearity and CT symmetry in the formation of defect modes. The measurements agree with the theory which predicts that, up to moderate pumping, the defect mode is an eigenstate of the CT-symmetric operator and retains its frequency at the center of the gap. At higher pumping values, the system undergoes a self-induced explicit CT-symmetry violation which removes the spectral topological protection and alters the shape of the defect mode.

We introduce a wave front shaping protocol for focusing inside disordered media based on a generalization of the established Wigner-Smith time-delay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specific experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength-ranging from strongly focusing on the designated target to completely bypassing it. Our protocol works without optimization or phase conjugation and we expect it to be particularly attractive for optical imaging in disordered media.

We present the first experimental observation of resonance-assisted tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly enhanced by the presence of a classical nonlinear resonance chain. For this we use a microwave cavity made of oxygen free copper with the shape of a desymmetrized cosine billiard designed with a large nonlinear resonance chain in the regular region. It is opened in a region, where only chaotic dynamics takes place, such that the tunneling rate of a regular mode to the chaotic region increases the line width of the mode. Resonance-assisted tunneling is demonstrated by (i) a parametric variation and (ii) the characteristic plateau and peak structure towards the semiclassical limit.

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to √N, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density-namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.

By means of a microwave tight-binding analogue experiment of a graphenelike lattice, we observe a topological transition between a phase with a pointlike 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.

We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex plane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.

We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix modeling, agrees perfectly with scattering echo measurements on a quasi-one-dimensional microwave cavity filled with randomly distributed scatterers.