arXiv subjects

U. Kuhl

Publications and source records attributed to U. Kuhl.

At least 19 recordsLinked to original sources

arXiv2021

Microwave studies of the three chiral ensembles in chains of coupled dielectric resonators

Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian orthogonal (GOE), Gaussian unitary (GUE), and Gaussian symplectic (GSE) one. With a further particle-antiparticle symmetry the chiral variants of these ensembles, the chiral orthogonal, unitary, and symplectic ensembles (the BDI, AIII, and CII in Cartan's notation) appear which are the main point of interest in this paper. Following a recently published work on chiral random matrix ensembles and their experimental realizations (Rehemanjiang et al., PRL 124, 116801 (2020)), this is achieved by using dielectric cylinders placed between two parallel aluminium plates. These cylinders act as microwave resonators which are used to create tight-binding chains of finite length up to N=5. The different ensembles are achieved by using different types of couplings: For the orthogonal case spatial proximity is used, for the unitary case microwave circulators are used, and for the symplectic case a combination of circulators and cables is used to create the necessary symmetry. In all cases the predicted repulsion behavior between positive and negative eigenvalues for energies close to zero are verified by a comparison with theory taking the finite size of the systems into account. We will show that the difference to the expected universal behavior is given by logarithmic corrections only. These corrections stem from the Hamiltonians having zero entries in their off-diagonal blocks.

cond-mat.mes-hall↗

arXiv2021

Microwave graphs analogs for the voltage drop in three-terminal devices with orthogonal, unitary and symplectic symmetry

Transmission measurements through three-port microwave graphs are performed in a symmetric setting, in analogy to three-terminal voltage drop devices with orthogonal, unitary, and symplectic symmetry. The terminal used as a probe is symmetrically located between two chaotic graphs, each graph is connected to one port, the input and the output, respectively. The analysis of the experimental data exhibit the weak localization and antilocalization phenomena in a clear fashion. We find a good agreement with theoretical predictions, provided that the effect of dissipation and imperfect coupling to the ports are taken into account.

cond-mat.other↗

arXiv2019

A microwave realization of the chiral orthogonal, unitary, and symplectic ensembles

cond-mat.mes-hall↗

arXiv2018

Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry

The Landauer-Büttiker formalism establishes an equivalence between the electrical conduction through a device, e.g., a quantum dot, and the transmission. Guided by this analogy we perform transmission measurements through three-port microwave graphs with orthogonal, unitary, and symplectic symmetry thus mimicking three-terminal voltage drop devices. One of the ports is placed as input and a second one as output, while a third port is used as a probe. Analytical predictions show good agreement with the measurements in the presence of orthogonal and unitary symmetries, provided that the absorption and the influence of the coupling port are taken into account. The symplectic symmetry is realized in specifically designed graphs mimicking spin 1/2 systems. Again a good agreement between experiment and theory is found. For the symplectic case the results are marginally sensitive to absorption and coupling strength of the port, in contrast to the orthogonal and unitary case.

cond-mat.mes-hall↗

arXiv2017

Spectra and spectral correlations of microwave graphs with symplectic symmetry

Following an idea by Joyner et al. [EPL, 107 (2014) 50004] a microwave graph with antiunitary symmetry T obeying T^2=-1 has been realized. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition results on the two-point correlation function, the spectral form factor, the number variance and the spectral rigidity are presented, as well as on the transition from GSE to GOE statistics by continuously changing T from T^2=-1 to T^2=1.

quant-ph↗

arXiv2016

A microwave realization of the Gaussian symplectic ensemble

Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)] a microwave graph with an antiunitary symmetry T obeying T^2=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry.

cond-mat.dis-nn↗

arXiv2016

Waveguide photonic limiters based on topologically protected resonant modes

We propose a concept of chiral photonic limiters utilising topologically protected localised midgap defect states in a photonic waveguide. The chiral symmetry alleviates the effects of structural imperfections and guaranties a high level of resonant transmission for low intensity radiation. At high intensity, the light-induced absorption can suppress the localised modes, along with the resonant transmission. In this case the entire photonic structure becomes highly reflective within a broad frequency range, thus increasing dramatically the damage threshold of the limiter. Here we demonstrate experimentally the principle of operation of such photonic structures using a waveguide consisting of coupled dielectric microwave resonators.

physics.optics↗

arXiv2016

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

cond-mat.mes-hall↗

arXiv2015

Selective enhancement of topologically induced interface states in a dielectric resonator chain

The recent realization of topological phases in insulators and superconductors has advanced the quest for robust quantum technologies. The prospects to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including couplers, rectifiers and lasers.

physics.optics↗

arXiv2014

Experimental Width Shift Distribution: A Test of Nonorthogonality for Local and Global Perturbations

The change of resonance widths in an open system under a perturbation of its interior has been recently introduced by Fyodorov and Savin [Phys. Rev. Lett. 108, 184101 (2012)] as a sensitive indicator of the nonorthogonality of resonance states. We experimentally study universal statistics of this quantity in weakly open two-dimensional microwave cavities and reverberation chambers realizing scalar and electromagnetic vector fields, respectively. We consider global as well as local perturbations, and also extend the theory to treat the latter case. The influence of the perturbation type on the width shift distribution is more pronounced for many-channel systems. We compare the theory to experimental results for one and two attached antennas and to numerical simulations with higher channel numbers, observing a good agreement in all cases.

cond-mat.mes-hall↗

arXiv2014

Statistics of the electromagnetic response of a chaotic reverberation chamber

This article presents a study of the electromagnetic response of a chaotic reverberation chamber (RC) in the presence of losses. By means of simulations and of experiments, the fluctuations in the maxima of the field obtained in a conventional mode-stirred RC are compared with those in a chaotic RC in the neighborhood of the Lowest Useable Frequency (LUF). The present work illustrates that the universal spectral and spatial statistical properties of chaotic RCs allow to meet more adequately the criteria required by the Standard IEC 61000-4-21 to perform tests of electromagnetic compatibility.

physics.data-an↗

arXiv2014

Formation and interaction of resonance chains in the open 3-disk system

In ballistic open quantum systems one often observes that the resonances in the complex-energy plane form a clear chain structure. Taking the open 3-disk system as a paradigmatic model system, we investigate how this chain structure is reflected in the resonance states and how it is connected to the underlying classical dynamics. Using an efficient scattering approach we observe that resonance states along one chain are clearly correlated while resonance states of different chains show an anticorrelation. Studying the phase space representations of the resonance states we find that their localization in phase space oscillate between different regions of the classical trapped set as one moves along the chains and that these oscillations are connected to a modulation of the resonance spacing. A single resonance chain is thus no WKB quantization of a single periodic orbits, but the structure of several oscillating chains arises from the interaction of several periodic orbits. We illuminate the physical mechanism behind these findings by combining the semiclassical cycle expansion with a quantum graph model.

cond-mat.dis-nn↗

arXiv2014

Spectral properties of microwave graphs with local absorption

The influence of absorption on the spectra of microwave graphs has been studied experimentally. The microwave networks were made up of coaxial cables and T junctions. First, absorption was introduced by attaching a 50 Ohm load to an additional vertex for graphs with and without time-reversal symmetry. The resulting level-spacing distributions were compared with a generalization of the Wigner surmise in the presence of open channels proposed recently by Poli et al. [Phys. Rev. Lett. 108, 174101 (2012)]. Good agreement was found using an effective coupling parameter. Second, absorption was introduced along one individual bond via a variable microwave attenuator, and the influence of absorption on the length spectrum was studied. The peak heights in the length spectra corresponding to orbits avoiding the absorber were found to be independent of the attenuation, whereas, the heights of the peaks belonging to orbits passing the absorber once or twice showed the expected decrease with increasing attenuation.

nlin.CD↗

arXiv2014

Transmission in waveguides with compositional and structural disorder: experimental effects of disorder cross-correlations

We analyse the single-mode transmission of microwaves in a guide with internal random structure. The waveguide contains scatterers characterised by random heights and positions, corresponding to compositional and structural disorder. We measure the effects of cross-correlations between two kinds of disorder, showing how they enhance or attenuate the experimentally found transmission gaps generated by long-range self-correlations. The results agree with the theoretical predictions obtained for the aperiodic Kronig-Penney model and prove that self- and cross-correlations have relevant effects also in finite disordered samples of small size.

cond-mat.mes-hall↗

arXiv2013

Schematic baryon models, their tight binding description and their microwave realization

A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and good agreement with the prediction is achieved.

nucl-th↗

arXiv2013

First experimental realization of the Dirac oscillator

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yields the spectrum of the one-dimensional Dirac oscillator with and without mass term. The flexibility of the experimental set-up allows the implementation of other one-dimensional Dirac type equations.

cond-mat.mes-hall↗

arXiv2013

Experimental Observation of a Fundamental Length Scale of Waves in Random Media

Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show numerically how the scintillation index can be used to assess the scaling behavior of the branching length. We report the experimental observation of this scaling using microwave transport experiments in quasi-two-dimensional resonators with randomly distributed weak scatterers. Remarkably, the scaling range extends much further than expected from random caustics statistics.

cond-mat.dis-nn↗

arXiv2013

Microwave realisation of a periodically driven system

A realisation of a periodically driven microwave system is presented. The principal element of the scheme is a variable capacity, i.e. a varicap, introduced as an element of the resonant circuit. Sideband structures corresponding to different driving signals, have been measured experimentally. In the linear regime we observed sideband structures with specific shapes. The main peculiarities of these shapes can be explained within a semiclassical approximation. A good agreement between experimental data and theoretical expectations has been found.

physics.class-ph↗