1
|
Dietz B, Klaus T, Masi M, Miski-Oglu M, Richter A, Skipa T, Wunderle M. Closed and open superconducting microwave waveguide networks as a model for quantum graphs. Phys Rev E 2024; 109:034201. [PMID: 38632749 DOI: 10.1103/physreve.109.034201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 02/08/2024] [Indexed: 04/19/2024]
Abstract
We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of equal width but incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one-dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds. The tetrahedral network comprises T junctions, while the honeycomb network exclusively consists of Y junctions, that join waveguides with relative angles 90^{∘} and 120^{∘}, respectively. We demonstrate that the vertex scattering matrix, which describes the propagation of the modes through the junctions, strongly depends on frequency and is nonsymmetric at a T junction and thus differs from that of a quantum graph with Neumann boundary conditions at the vertices. On the other hand, at a Y junction, similarity can be achieved in a certain frequency range. We investigate the spectral properties of closed waveguide networks and fluctuation properties of the scattering matrix of open ones and find good agreement with random matrix theory predictions for the honeycomb waveguide graph.
Collapse
Affiliation(s)
- Barbara Dietz
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Republic of Korea
| | - Tobias Klaus
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Marco Masi
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Maksym Miski-Oglu
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
| | - Achim Richter
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Tatjana Skipa
- Darmstadt University of Applied Sciences, D-64295 Darmstadt, Germany
| | - Marcus Wunderle
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| |
Collapse
|
2
|
Zhang X, Zhang W, Che J, Dietz B. Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics. Phys Rev E 2023; 108:044211. [PMID: 37978640 DOI: 10.1103/physreve.108.044211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 09/20/2023] [Indexed: 11/19/2023]
Abstract
We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T-invariance violation and chaoticity are induced by magnetizing a ferrite disk placed at its center, which above the cutoff frequency of the first transverse-electric mode acts as a random potential. We determine a complete sequence of ≃1000 eigenfrequencies and find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model, which interpolates between Poisson statistics expected for typical integrable systems and Gaussian unitary ensemble statistics predicted for chaotic systems with violated Tinvariance. Furthermore, we combine the RP model and the Heidelberg approach for quantum-chaotic scattering to construct a random-matrix model for the scattering (S) matrix of the corresponding open quantum system and show that it perfectly reproduces the fluctuation properties of the measured S matrix of the microwave resonator.
Collapse
Affiliation(s)
- Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Weihua Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Korea
| |
Collapse
|
3
|
Akhshani A, Białous M, Sirko L. Quantum graphs and microwave networks as narrow-band filters for quantum and microwave devices. Phys Rev E 2023; 108:034219. [PMID: 37849123 DOI: 10.1103/physreve.108.034219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2023] [Accepted: 09/19/2023] [Indexed: 10/19/2023]
Abstract
We investigate properties of the transmission amplitude of quantum graphs and microwave networks composed of regular polygons such as triangles and squares. We show that for the graphs composed of regular polygons, with the edges of the length l, the transmission amplitude displays a band of transmission suppression with some narrow peaks of full transmission. The peaks are distributed symmetrically with respect to the symmetry axis kl=π, where k is the wave vector. For microwave networks the transmission peak amplitudes are reduced and their symmetry is broken due to the influence of internal absorption. We demonstrate that for the graphs composed of the same polygons but separated by the edges of length l^{'}
Collapse
Affiliation(s)
- Afshin Akhshani
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| |
Collapse
|
4
|
Białous M, Dietz B, Sirko L. Experimental study of the elastic enhancement factor in a three-dimensional wave-chaotic microwave resonator exhibiting strongly overlapping resonances. Phys Rev E 2023; 107:054210. [PMID: 37328966 DOI: 10.1103/physreve.107.054210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/24/2023] [Indexed: 06/18/2023]
Abstract
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.
Collapse
Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| |
Collapse
|
5
|
Ławniczak M, Akhshani A, Farooq O, Białous M, Bauch S, Dietz B, Sirko L. Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption. Phys Rev E 2023; 107:024203. [PMID: 36932527 DOI: 10.1103/physreve.107.024203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Accepted: 01/24/2023] [Indexed: 02/09/2023]
Abstract
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.
Collapse
Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Afshin Akhshani
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Omer Farooq
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Szymon Bauch
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.,Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| |
Collapse
|
6
|
Ma S, Antonsen TM, Anlage SM. Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs. Phys Rev E 2022; 106:054215. [PMID: 36559373 DOI: 10.1103/physreve.106.054215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a physical setting for chaotic graph studies. Photonic crystal waveguides possess a dispersion relation for the propagating modes, which is engineerable. Graphs constructed by joining these waveguides possess junctions and bends with distinct scattering properties. We present numerically determined statistical properties of an ensemble of such PC graphs including both eigenfunction amplitude and eigenmode-spacing studies. Our proposed system is compatible with silicon nanophotonic technology and opens chaotic graph studies to a new community of researchers.
Collapse
Affiliation(s)
- Shukai Ma
- Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Thomas M Antonsen
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742-3285, USA
| | - Steven M Anlage
- Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742-3285, USA
| |
Collapse
|
7
|
Zhang W, Zhang X, Che J, Lu J, Miski-Oglu M, Dietz B. Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance. Phys Rev E 2022; 106:044209. [PMID: 36397497 DOI: 10.1103/physreve.106.044209] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
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 wave number 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 framework of random matrix theory for quantum chaotic scattering systems.
Collapse
Affiliation(s)
- Weihua Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Junjie Lu
- Institut de Physique de Nice, CNRS UMR 7010, Université Côte d'Azur, 06108 Nice, France
| | - M Miski-Oglu
- GSI Helmholtzzentrum für Schwerionenforschung GmbH D-64291 Darmstadt, Germany
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| |
Collapse
|
8
|
Che J, Zhang X, Zhang W, Dietz B, Chai G. Fluctuation properties of the eigenfrequencies and scattering matrix of closed and open unidirectional graphs with chaotic wave dynamics. Phys Rev E 2022; 106:014211. [PMID: 35974604 DOI: 10.1103/physreve.106.014211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
We present experimental and numerical results for the fluctuation properties in the eigenfrequency spectra and of the scattering matrix of closed and open unidirectional quantum graphs, respectively. Unidirectional quantum graphs, that are composed of bonds connected by reflectionless vertices, were introduced by Akila and Gutkin [Akila and Gutkin, J. Phys. A: Math. Theor. 48, 345101 (2015)1751-811310.1088/1751-8113/48/34/345101]. The nearest-neighbor spacing distribution of their eigenvalues was shown to comply with random-matrix theory predictions for typical chaotic systems with completely violated time-reversal invariance. The occurrence of short periodic orbits confined to a fraction of the system, that lead in conventional quantum graphs to deviations of the long-range spectral correlations from the behavior expected for typical chaotic systems, is suppressed in unidirectional ones. Therefore, we pose the question whether such graphs may serve as a more appropriate model for closed and open chaotic systems with violated time-reversal invariance than conventional ones. We compare the fluctuation properties of their eigenvalues and scattering matrix elements and observe especially in the long-range correlations larger deviations from random-matrix theory predictions for the unidirectional graphs. These are attributed to a loss of complexity of the underlying dynamic, induced by the unidirectionality.
Collapse
Affiliation(s)
- Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Weihua Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Guozhi Chai
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| |
Collapse
|
9
|
Białous M, Dietz B, Sirko L. Missing-level statistics in a dissipative microwave resonator with partially violated time-reversal invariance. Phys Rev E 2021; 103:052204. [PMID: 34134203 DOI: 10.1103/physreve.103.052204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 04/19/2021] [Indexed: 11/07/2022]
Abstract
We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal-invariance violation (TIV) which is induced by two magnetized ferrites. The cavity has the shape of a quarter bowtie billiard of which the corresponding classical dynamics is chaotic. Due to dissipation it is impossible to identify a complete list of resonance frequencies. Based on a random-matrix theory approach we derive analytical expressions for statistical measures of short- and long-range correlations in such incomplete spectra interpolating between the cases of preserved time-reversal invariance and complete TIV and demonstrate their applicability to the experimental spectra.
Collapse
Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| |
Collapse
|