Channel cross-correlations in transport through complex media

Measuring transmission between four antennas in microwave cavities, we investigate directly the channel cross-correlations $C$ of the cross sections $\sigma^{ab}$ from antenna at $\vec{r}_a$ to antenna $\vec{r}_b$. Specifically we look for the $C_\Sigma$ and $C_\Lambda$, where the only difference is that $C_\Lambda$ has none of the four channels in common, whereas $C_\Sigma$ has exactly one channel in common. We find experimentally that these two channel cross-correlations are anti-phased as a function of the channel coupling strength, as predicted by theory. This anti-correlation is essential to give the correct values for the universal conductance fluctuations. To obtain a good agreement between experiment and predictions from random matrix theory the effect of absorption had to be included.Comment: 6 pages, 5 figure

Experimental Observation of Resonance-Assisted Tunneling

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.Comment: 5 pages, 2 figure

Continuity Equation for the Flow of Fisher Information in Wave Scattering

Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information as possible about an object of interest by sending a probing wave at it and processing the information delivered back to the detector. Here, we demonstrate that an electromagnetic wave scattered at an object carries locally defined and conserved information about all of the object's constitutive parameters. Specifically, we introduce here the density and flux of Fisher information for very general types of wave fields and identify corresponding sources and sinks of information through which all these new quantities satisfy a fundamental continuity equation. We experimentally verify our theoretical predictions by studying a movable object embedded inside a disordered environment and by measuring the corresponding Fisher information flux at microwave frequencies. Our results provide a new understanding of the generation and propagation of information and open up new possibilities for tracking and designing the flow of information even in complex environments.Comment: 17 pages, 4 figures, plus a methods section and supplementary materia

Microwave experiments simulating quantum search and directed transport in artificial graphene

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to \sqrt{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

Fano resonances and decoherence in transport through quantum dots

A tunable microwave scattering device is presented which allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. We observe a non-monotonic evolution of resonance parameters that is explained in terms of interacting resonances. The dissipation of radiation in the cavity walls leads to decoherence and thus to a modification of the Fano profile. We show that the imaginary part of the complex Fano q-parameter allows to determine the absorption constant of the cavity. Our theoretical results demonstrate further that the two decohering mechanisms, dephasing and dissipation, are equivalent in terms of their effect on the evolution of Fano resonance lineshapes.Comment: 9 pages, 7 figures, submitted to Physica E (conference proceedings