arXiv subjects

Hans-Jürgen Stöckmann

Publications and source records attributed to Hans-Jürgen Stöckmann.

11 recordsLinked to original sources

arXiv2024

Spin resonance without a spin: A microwave analog

An analog of nuclear magnetic resonance is realized in a microwave network with symplectic symmetry. The network consists of two identical subgraphs coupled by a pair of bonds with a length difference corresponding to a phase difference of $π$ for the waves traveling through the bonds. As a consequence all eigenvalues appear as Kramers doublets. Detuning the length difference from the $π$ condition Kramers degeneracy is lifted, which may be interpreted as a Zeeman splitting of a spin 1/2 in a magnetic field. The lengths of another pair of bonds are modulated periodically with frequencies of some 10 MHz by means of diodes, thus emulating a magnetic radiofrequency field. Features well-known from NMR such as the transition from the laboratory to the rotating frame, and Lorentzian shaped resonance curves can thus be realized.

physics.app-ph↗

arXiv2024

Non-Weyl Behavior Induced by Superradiance: A Microwave Graph Study

We study experimentally the manifestation of non-Weyl graph behavior in open systems using microwave networks. For this a coupling variation to the network is necessary, which was out of reach till now. The coupling to the environment is changed by indirectly varying the boundary condition at the coupling vertex from Dirichlet to Neumann using a dangling bond with variable length attached the coupling vertex. A transformation of equal length spectra to equal reflection phase spectra of the dangling bond allows to create spectra with different fixed coupling strength. This allows to follow the resonances in the complex plane as a function of the coupling. While going from closed (Dirichlet) to fully open (Neumann) graph we see resonances escaping via a superradiant transition leading to non-Weyl behavior if the coupling to the outside is balanced. The open tetrahedral graph displays a rich parametric dynamic of the resonances in the complex plane presenting loops, regions of connected resonances and resonances approaching infinite imaginary parts.

physics.class-ph↗

arXiv2021

A spectral duality in graphs and microwave networks

Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and charge conservation. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The first ones are realized in experiments, since the standard junctions connecting the bonds obey Neumann boundary conditions due to current conservation. On average, the corresponding Neumann and Dirichlet eigenvalues alternate as a function of the wave number, with the consequence that the Neumann spectrum is described by random matrix theory only locally, but adopts features of the interlacing Dirichlet spectrum for long-range correlations. Another spectral interlacing is found for the Green's function, which in contrast to the secular determinant is experimentally accessible. This is illustrated by microwave studies and numerics.

cond-mat.mes-hall↗

arXiv2015

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.

cond-mat.mes-hall↗

arXiv2015

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.

cond-mat.mes-hall↗

arXiv2015

Compounding approach for univariate time series with non-stationary variances

A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model the long-term statistical behavior, we compound the local distribution with the distribution of its parameters. Here we consider two concrete, but diverse examples of such non-stationary systems, the turbulent air flow of a fan and a time series of foreign exchange rates. Our main focus is to empirically determine the appropriate parameter distribution for the compounding approach. To this end we have to estimate the parameter distribution for univariate time series in a highly non-stationary situation.

physics.data-an↗

arXiv2012

Universal Quantum Localizing Transition of a Partial Barrier in a Chaotic Sea

Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >> Phi, such that wave packets and states are localized. In contrast, classical transport is mimicked for h << Phi. Designing a quantum map with an isolated partial barrier of controllable flux Phi is the key to investigating the transition from this form of quantum localization to mimicking classical transport. It is observed that quantum transport follows a universal transition curve as a function of the expected scaling parameter Phi/h. We find this curve to be symmetric to Phi/h=1, having a width of two orders of magnitude in Phi/h, and exhibiting no quantized steps. We establish the relevance of local coupling, improving on previous random matrix models relying on global coupling. It turns out that a phenomenological 2x2-model gives an accurate analytical description of the transition curve.

nlin.CD↗

arXiv2011

Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents

We study fidelity decay in classically chaotic microwave billiards for a local, piston-like boundary perturbation. We experimentally verify a predicted non-monotonic cross-over from the Fermi Golden Rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations.

nlin.CD↗

arXiv2010

Measurement of the Goos-Hänchen shift in a microwave cavity

We present measurements of the Goos-Hänchen shift in a two-dimensional dielectric microwave cavity. Microwave beams are generated by a suitable superposition of the spherical waves generated by an array of antennas; the resulting beams are then reflected at a planar interface. By measuring the electric field including its phase, Poynting vectors of the incoming and reflected beams can be extracted, which in turn are used to find the incoming angle and the positions where the beam hits the interface and where it is reflected. These positions directly yield the Goos-Hänchen shift. The results are compared to the classical Artmann result and a numerical calculation using Gaussian beams.

physics.optics↗

arXiv2010

Probing decoherence through Fano resonances

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.

cond-mat.mes-hall↗

arXiv2009

Probing Localization in Absorbing Systems via Loschmidt Echos

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.

cond-mat.dis-nn↗