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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.
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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
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Isoscattering strings of concatenating graphs and networks. Sci Rep 2021; 11:1575. [PMID: 33452312 PMCID: PMC7810996 DOI: 10.1038/s41598-020-80950-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2020] [Accepted: 12/30/2020] [Indexed: 11/08/2022] Open
Abstract
We identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for \documentclass[12pt]{minimal}
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\begin{document}$$n \rightarrow \infty $$\end{document}n→∞. The theoretical predictions are confirmed experimentally using \documentclass[12pt]{minimal}
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\begin{document}$$n=2$$\end{document}n=2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the \documentclass[12pt]{minimal}
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\begin{document}$$2n \times 2n $$\end{document}2n×2n scattering matrices \documentclass[12pt]{minimal}
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\begin{document}$${\hat{S}}$$\end{document}S^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all \documentclass[12pt]{minimal}
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\begin{document}$$(2n)^2$$\end{document}(2n)2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.
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Ławniczak M, van Tiggelen B, Sirko L. Experimental investigation of distributions of the off-diagonal elements of the scattering matrix and Wigner's K[over ̂] matrix for networks with broken time reversal invariance. Phys Rev E 2020; 102:052214. [PMID: 33327135 DOI: 10.1103/physreve.102.052214] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 11/03/2020] [Indexed: 11/07/2022]
Abstract
We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix S[over ̂] and the Wigner's reaction K[over ̂] matrix for open microwave networks with broken time (T) reversal invariance. Microwave Faraday circulators were applied in order to break T invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix S[over ̂] are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, and T. Guhr, Ann. Phys. (NY) 342, 103 (2014)10.1016/j.aop.2013.11.006]. Furthermore, we show that the experimental results are in very good agreement with the recent predictions for the distributions of the real and imaginary parts of the off-diagonal elements of the Wigner's reaction K[over ̂] matrix obtained within the framework of the Gaussian unitary ensemble of random matrix theory [S. B. Fedeli and Y. V. Fyodorov, J. Phys. A: Math. Theor. 53, 165701 (2020)1751-811310.1088/1751-8121/ab73ab]. Both theories include losses as tunable parameters and are therefore well adapted to the experimental verification.
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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | | | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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Investigation of the diagonal elements of the Wigner's reaction matrix for networks with violated time reversal invariance. Sci Rep 2019; 9:5630. [PMID: 30948771 PMCID: PMC6449383 DOI: 10.1038/s41598-019-42123-y] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2018] [Accepted: 03/25/2019] [Indexed: 11/11/2022] Open
Abstract
The distributions of the diagonal elements of the Wigner’s reaction \documentclass[12pt]{minimal}
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\begin{document}$$\hat{K}$$\end{document}Kˆ matrix for open systems with violated time reversal T invariance in the case of large absorption are for the first time experimentally studied. The Wigner’s reaction matrix links the properties of chaotic systems with the scattering processes in the asymptotic region. Microwave networks consisting of microwave circulators were used in the experiment to simulate quantum graphs with violated T invariance. The distributions of the diagonal elements of the reaction \documentclass[12pt]{minimal}
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\begin{document}$$\hat{K}$$\end{document}Kˆ matrix were experimentally evaluated by measuring of the two-port scattering matrix \documentclass[12pt]{minimal}
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\begin{document}$$\hat{S}$$\end{document}Sˆ. The violation of T invariance in the networks with large absorption was demonstrated by calculating the enhancement factor W of the matrix \documentclass[12pt]{minimal}
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\begin{document}$$\hat{S}$$\end{document}Sˆ. Our experimental results are in very good agreement with the analytic ones attained for the Gaussian unitary ensemble in the random matrix theory. The obtained results suggest that the distributions P(ʋ) and P(u) of the imaginary and the real parts of the diagonal elements of the Wigner’s reaction \documentclass[12pt]{minimal}
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\begin{document}$$\hat{K}$$\end{document}Kˆ matrix together with the enhancement factor W can be used as a powerful tool for identification of systems with violated T symmetry and quantification of their absorption.
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Cottet A, Dartiailh MC, Desjardins MM, Cubaynes T, Contamin LC, Delbecq M, Viennot JJ, Bruhat LE, Douçot B, Kontos T. Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:433002. [PMID: 28925381 DOI: 10.1088/1361-648x/aa7b4d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
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Affiliation(s)
- Audrey Cottet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS UMR 8551, Laboratoire associé aux universités Pierre et Marie Curie et Denis Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France
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Gagnon D, Fillion-Gourdeau F, Dumont J, Lefebvre C, MacLean S. Suppression of Multiphoton Resonances in Driven Quantum Systems via Pulse Shape Optimization. PHYSICAL REVIEW LETTERS 2017; 119:053203. [PMID: 28949713 DOI: 10.1103/physrevlett.119.053203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2017] [Indexed: 06/07/2023]
Abstract
This Letter demonstrates control over multiphoton absorption processes in driven two-level systems, which include, for example, superconducting qubits or laser-irradiated graphene, through spectral shaping of the driving pulse. Starting from calculations based on Floquet theory, we use differential evolution, a general purpose optimization algorithm, to find the Fourier coefficients of the driving function that suppress a given multiphoton resonance in the strong field regime. We show that the suppression of the transition probability is due to the coherent superposition of high-order Fourier harmonics which closes the dynamical gap between the Floquet states of the two-level system.
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Affiliation(s)
- Denis Gagnon
- Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada, J3X 1S2
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - François Fillion-Gourdeau
- Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada, J3X 1S2
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Joey Dumont
- Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada, J3X 1S2
| | - Catherine Lefebvre
- Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada, J3X 1S2
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Steve MacLean
- Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada, J3X 1S2
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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