Barbara Dietz - Academia.edu (original) (raw)

Papers by Barbara Dietz

Acta Physica Polonica A, Dec 1, 2021

Acta Physica Polonica A, Nov 1, 2019

Physical review, Apr 19, 2021

Acta Physica Polonica A, Nov 1, 2019

arXiv (Cornell University), Jun 2, 2023

Acta Physica Polonica A, Dec 1, 2021

Physical Review C, Nov 20, 2018

CLEO 2023

Möbius strip microlasers are fabricated by direct laser writing. Experiments and 3D FDTD numerica... more Möbius strip microlasers are fabricated by direct laser writing. Experiments and 3D FDTD numerical simulations evidence that laser modes propagate along periodic geodesics, a geodesic being the shortest path between two points on a surface.

arXiv: Statistical Mechanics, 2020

This article is dedicated to the following class of problems. Start with an NtimesNN\times NNtimesN Hermitian... more This article is dedicated to the following class of problems. Start with an NtimesNN\times NNtimesN Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with ttt taking the values 1letleN1\le t \le N1letleN, we study the difference between the spectra of the perturbed and the reference matrices as a function of ttt and its dependence on the underlying universality class of the random matrix ensemble. We consider both, the weaker kind of perturbation which either permutes or randomizes ttt diagonal elements and a stronger perturbation randomizing successively ttt rows and columns. In the first case we derive universal expressions in the scaled parameter tau=t/N\tau=t/Ntau=t/N for the expectation of the variance of the spectral shift functions, choosing as random-matrix ensembles Dyson's three Gaussian ensembles. In the second case we find an additional dependence on the matrix size NNN.

Physical review, Apr 27, 2023

Physical review, Oct 20, 2022

We report on experiments that were performed with microwave waveguide systems and demonstrate tha... more We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equation with boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wavenumber and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the frame work of random matrix theory for quantum chaotic scattering systems.

arXiv (Cornell University), Feb 16, 2023

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that ... more We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational (C3) symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure which we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by 2π 3 into the three C3 subspaces. This allows us to verify previous numerical results of Ref. [W. Zhang and B. Dietz, Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and are well described by a tight-binding model (TBM) for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions, where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterpart.

Physical review, May 13, 2021

We present an in-depth study of the universal correlations of scattering-matrix entries required ... more We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of non-stationary many-body scattering where the incoming states are localized wavepackets. Contrary to the stationary case the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.

Acta Physica Polonica A, Dec 1, 2017

We present experimental and numerical studies for level statistics in incomplete spectra obtained... more We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.

Physical Review E

We study the elastic enhancement factor and the two-point correlation function of the scattering ... more We study the elastic enhancement factor and the two-point correlation function of the scattering matrix obtained from measurements of reflection and transmission spectra of a three-dimensional (3D) wave-chaotic microwave cavity in regions of moderate and large absorption. They are used to identify the degree of chaoticity of the system in the presence of strongly overlapping resonances, where other measures such as short-and long-range level correlations cannot be applied. The average value of the experimentally determined elastic enhancement factor for two scattering channels agrees well with random-matrix theory predictions for quantum chaotic systems, thus corroborating that the 3D microwave cavity exhibits the features of a fully chaotic system with preserved time-reversal invariance. To confirm this finding we analyzed spectral properties in the frequency range of lowest achievable absorption using missing-level statistics.

Physical Review E

We report on experimental studies of the distribution of the reflection coefficients, and the ima... more We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, and attributed to the presence of nonuniversal short periodic orbits, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.

Physical Review E

We report on the experimental investigation of the dependence of the elastic enhancement, i.e., e... more We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in backward direction over scattering in other directions of a wave-chaotic system with partially violated time-reversal (T) invariance on its openness. The elastic enhancement factor is a characteristic of quantum chaotic scattering which is of particular importance in experiments, like compound-nuclear reactions, where only cross sections, i.e., the moduli of the associated scattering matrix elements are accessible. In the experiment a quantum billiard with the shape of a quarter bow-tie, which generates a chaotic dynamics, is emulated by a flat microwave cavity. Partial T-invariance violation of varying strength 0 ≤ ξ 1 is induced by two magnetized ferrites. The openness is controlled by increasing the number M of open channels, 2 ≤ M ≤ 9, while keeping the internal absorption unchanged. We investigate the elastic enhancement as function of ξ and find that for a fixed M it decreases with increasing time-reversal invariance violation, whereas it increases with increasing openness beyond a certain value of ξ 0.2. The latter result is surprising because it is opposite to that observed in systems with preserved T invariance (ξ = 0). We come to the conclusion that the effect of T-invariance violation on the elastic enhancement then dominates over the openness, which is crucial for experiments which rely on enhanced backscattering, since, generally, a decrease of the openness is unfeasible. Motivated by these experimental results we, furthermore, performed theoretical investigations based on random matrix theory which confirm our findings.

EPL (Europhysics Letters), 2019

Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave... more Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave dynamics and geometric optics in resonators. However, the mode structures of three-dimensional microlasers without rotational symmetry remain largely unexplored due to fabrication limitations. Previous studies of such cavities revealed lasing modes localized on periodic orbits exclusively confined to a single plane. In this work, we report on the characterization of pyramidal, polymer-based microlasers and demonstrate that the lasing modes are localized on a genuine three-dimensional periodic orbit. The consequences on the laser features are further discussed, in particular stability and polarization issues.

Physical Review A, 2018

A major objective in photonics is to tailor the emission properties of microcavities which is usu... more A major objective in photonics is to tailor the emission properties of microcavities which is usually achieved with specific cavity shapes. Yet, the dynamical change of the emission properties during operation would often be advantageous. The implementation of such a method is still a challenging issue. We present an effective procedure for the dynamical control of the emission lobes which relies on the selection of a specific coherent superposition of degenerate modes belonging to different symmetry classes. It is generally applicable to systems exhibiting pairs of degenerate modes. We explored it experimentally and analytically with organic square microlasers, which emit narrow lobes parallel to their sidewalls. By means of the pump polarization, emission lobes are switched on and off selectively with an extinction ratio better than 1/50.

Acta Physica Polonica A, Dec 1, 2021

Acta Physica Polonica A, Nov 1, 2019

Physical review, Apr 19, 2021

Acta Physica Polonica A, Nov 1, 2019

arXiv (Cornell University), Jun 2, 2023

Acta Physica Polonica A, Dec 1, 2021

Physical Review C, Nov 20, 2018

CLEO 2023

Möbius strip microlasers are fabricated by direct laser writing. Experiments and 3D FDTD numerica... more Möbius strip microlasers are fabricated by direct laser writing. Experiments and 3D FDTD numerical simulations evidence that laser modes propagate along periodic geodesics, a geodesic being the shortest path between two points on a surface.

arXiv: Statistical Mechanics, 2020

This article is dedicated to the following class of problems. Start with an NtimesNN\times NNtimesN Hermitian... more This article is dedicated to the following class of problems. Start with an NtimesNN\times NNtimesN Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with ttt taking the values 1letleN1\le t \le N1letleN, we study the difference between the spectra of the perturbed and the reference matrices as a function of ttt and its dependence on the underlying universality class of the random matrix ensemble. We consider both, the weaker kind of perturbation which either permutes or randomizes ttt diagonal elements and a stronger perturbation randomizing successively ttt rows and columns. In the first case we derive universal expressions in the scaled parameter tau=t/N\tau=t/Ntau=t/N for the expectation of the variance of the spectral shift functions, choosing as random-matrix ensembles Dyson's three Gaussian ensembles. In the second case we find an additional dependence on the matrix size NNN.

Physical review, Apr 27, 2023

Physical review, Oct 20, 2022

We report on experiments that were performed with microwave waveguide systems and demonstrate tha... more We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equation with boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wavenumber and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the frame work of random matrix theory for quantum chaotic scattering systems.

arXiv (Cornell University), Feb 16, 2023

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that ... more We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational (C3) symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure which we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by 2π 3 into the three C3 subspaces. This allows us to verify previous numerical results of Ref. [W. Zhang and B. Dietz, Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and are well described by a tight-binding model (TBM) for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions, where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterpart.

Physical review, May 13, 2021

We present an in-depth study of the universal correlations of scattering-matrix entries required ... more We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of non-stationary many-body scattering where the incoming states are localized wavepackets. Contrary to the stationary case the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.

Acta Physica Polonica A, Dec 1, 2017

We present experimental and numerical studies for level statistics in incomplete spectra obtained... more We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.

Physical Review E

We study the elastic enhancement factor and the two-point correlation function of the scattering ... more We study the elastic enhancement factor and the two-point correlation function of the scattering matrix obtained from measurements of reflection and transmission spectra of a three-dimensional (3D) wave-chaotic microwave cavity in regions of moderate and large absorption. They are used to identify the degree of chaoticity of the system in the presence of strongly overlapping resonances, where other measures such as short-and long-range level correlations cannot be applied. The average value of the experimentally determined elastic enhancement factor for two scattering channels agrees well with random-matrix theory predictions for quantum chaotic systems, thus corroborating that the 3D microwave cavity exhibits the features of a fully chaotic system with preserved time-reversal invariance. To confirm this finding we analyzed spectral properties in the frequency range of lowest achievable absorption using missing-level statistics.

Physical Review E

We report on experimental studies of the distribution of the reflection coefficients, and the ima... more We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, and attributed to the presence of nonuniversal short periodic orbits, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.

Physical Review E

We report on the experimental investigation of the dependence of the elastic enhancement, i.e., e... more We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in backward direction over scattering in other directions of a wave-chaotic system with partially violated time-reversal (T) invariance on its openness. The elastic enhancement factor is a characteristic of quantum chaotic scattering which is of particular importance in experiments, like compound-nuclear reactions, where only cross sections, i.e., the moduli of the associated scattering matrix elements are accessible. In the experiment a quantum billiard with the shape of a quarter bow-tie, which generates a chaotic dynamics, is emulated by a flat microwave cavity. Partial T-invariance violation of varying strength 0 ≤ ξ 1 is induced by two magnetized ferrites. The openness is controlled by increasing the number M of open channels, 2 ≤ M ≤ 9, while keeping the internal absorption unchanged. We investigate the elastic enhancement as function of ξ and find that for a fixed M it decreases with increasing time-reversal invariance violation, whereas it increases with increasing openness beyond a certain value of ξ 0.2. The latter result is surprising because it is opposite to that observed in systems with preserved T invariance (ξ = 0). We come to the conclusion that the effect of T-invariance violation on the elastic enhancement then dominates over the openness, which is crucial for experiments which rely on enhanced backscattering, since, generally, a decrease of the openness is unfeasible. Motivated by these experimental results we, furthermore, performed theoretical investigations based on random matrix theory which confirm our findings.

EPL (Europhysics Letters), 2019

Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave... more Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave dynamics and geometric optics in resonators. However, the mode structures of three-dimensional microlasers without rotational symmetry remain largely unexplored due to fabrication limitations. Previous studies of such cavities revealed lasing modes localized on periodic orbits exclusively confined to a single plane. In this work, we report on the characterization of pyramidal, polymer-based microlasers and demonstrate that the lasing modes are localized on a genuine three-dimensional periodic orbit. The consequences on the laser features are further discussed, in particular stability and polarization issues.

Physical Review A, 2018

A major objective in photonics is to tailor the emission properties of microcavities which is usu... more A major objective in photonics is to tailor the emission properties of microcavities which is usually achieved with specific cavity shapes. Yet, the dynamical change of the emission properties during operation would often be advantageous. The implementation of such a method is still a challenging issue. We present an effective procedure for the dynamical control of the emission lobes which relies on the selection of a specific coherent superposition of degenerate modes belonging to different symmetry classes. It is generally applicable to systems exhibiting pairs of degenerate modes. We explored it experimentally and analytically with organic square microlasers, which emit narrow lobes parallel to their sidewalls. By means of the pump polarization, emission lobes are switched on and off selectively with an extinction ratio better than 1/50.