1
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Fei J, Zhang X, Zhang Q, Yang Y, Wang Z, Deng C, Huang Y, Wang T. Exceptional point enhanced nanoparticle detection in deformed Reuleaux-triangle microcavity. FRONTIERS OF OPTOELECTRONICS 2024; 17:27. [PMID: 39115622 PMCID: PMC11310378 DOI: 10.1007/s12200-024-00131-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Accepted: 07/03/2024] [Indexed: 08/11/2024]
Abstract
In this paper, we propose a deformed Reuleaux-triangle resonator (RTR) to form exceptional point (EP) which results in the detection sensitivity enhancement of nanoparticle. After introducing single nanoparticle to the deformed RTR at EP, frequency splitting obtains an enhancement of more than 6 times compared with non-deformed RTR. In addition, EP induced a result that the far field pattern of chiral mode responses significantly to external perturbation, corresponding to the change in internal chirality. Therefore, single nanoparticle with far distance of more than 4000 nm can be detected by measuring the variation of far field directional emission. Compared to traditional frequency splitting, the far field pattern produced in deformed RTR provides a cost-effective and convenient path to detect single nanoparticle at a long distance, without using tunable laser and external coupler. Our structure indicates great potential in high sensitivity sensor and label-free detector.
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Affiliation(s)
- Jinhao Fei
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
| | - Xiaobei Zhang
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China.
| | - Qi Zhang
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
| | - Yong Yang
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
| | - Zijie Wang
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
| | - Chuanlu Deng
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
| | - Yi Huang
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
| | - Tingyun Wang
- Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, School of Communication and Information Engineering, Shanghai University, Shanghai, 200444, China
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2
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Keshavamurthy S. Dynamical Tunneling in More than Two Degrees of Freedom. ENTROPY (BASEL, SWITZERLAND) 2024; 26:333. [PMID: 38667887 PMCID: PMC11049088 DOI: 10.3390/e26040333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 04/08/2024] [Accepted: 04/10/2024] [Indexed: 04/28/2024]
Abstract
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose-Einstein condensates trapped in optical lattices.
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Affiliation(s)
- Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India
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3
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Park KW, Kim J, Seo J, Moon S, Jeong K, An K. Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard. CHAOS (WOODBURY, N.Y.) 2022; 32:103101. [PMID: 36319274 DOI: 10.1063/5.0101495] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 09/05/2022] [Indexed: 06/16/2023]
Abstract
We investigate two types of avoided crossings in a chaotic billiard within the framework of information theory. The Shannon entropy in the phase space for the Landau-Zener interaction increases as the center of the avoided crossing is approached, whereas for the Demkov interaction, the Shannon entropy decreases as the center of avoided crossing is passed by with an increase in the deformation parameter. This feature can provide a new indicator for scar formation. In addition, it is found that the Fisher information of the Landau-Zener interaction is significantly larger than that of the Demkov interaction.
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Affiliation(s)
- K-W Park
- Research Institute of Mathematics, Seoul National University, Seoul 08826, South Korea
| | - J Kim
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, South Korea
| | - J Seo
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, South Korea
| | - S Moon
- Faculty of Liberal Education, Seoul National University, Seoul 08826, South Korea
| | - K Jeong
- Research Institute of Mathematics, Seoul National University, Seoul 08826, South Korea
| | - K An
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, South Korea
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4
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Moon S, Shin Y, Kim S, Park KW, An K. Simultaneous determination of the shape and refractive index of a deformed microjet cavity from its resonances. OPTICS EXPRESS 2022; 30:13294-13304. [PMID: 35472945 DOI: 10.1364/oe.455326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2022] [Accepted: 03/22/2022] [Indexed: 06/14/2023]
Abstract
Measuring the boundary shape of a deformed liquid microjet is of great importance for using it as an optical resonator for various applications. However, there have been technical challenges due to transparency and uncertainty in the refractive index of the liquid. In this study, we have developed a spectroscopic technique that enables simultaneous determination of the boundary shape and the refractive index of a liquid deformed microjet. A detailed procedure of the technique based on imposition of one-to-one correspondence between experimentally observed resonances and numerically calculated ones are presented along with the measurement results including the refractive index of ethanol between a wavelength of 550 nm and 670 nm.
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5
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Wang S, Liu S, Liu Y, Xiao S, Wang Z, Fan Y, Han J, Ge L, Song Q. Direct observation of chaotic resonances in optical microcavities. LIGHT, SCIENCE & APPLICATIONS 2021; 10:135. [PMID: 34188015 PMCID: PMC8241958 DOI: 10.1038/s41377-021-00578-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Revised: 06/15/2021] [Accepted: 06/17/2021] [Indexed: 05/29/2023]
Abstract
Optical microcavities play a significant role in the study of classical and quantum chaos. To date, most experimental explorations of their internal wave dynamics have focused on the properties of their inputs and outputs, without directly interrogating the dynamics and the associated mode patterns inside. As a result, this key information is rarely retrieved with certainty, which significantly restricts the verification and understanding of the actual chaotic motion. Here we demonstrate a simple and robust approach to directly and rapidly map the internal mode patterns in chaotic microcavities. By introducing a local index perturbation through a pump laser, we report a spectral response of optical microcavities that is proportional to the internal field distribution. With this technique, chaotic modes with staggered mode spacings can be distinguished. Consequently, a complete chaos assisted tunneling (CAT) and its time-reversed process are experimentally verified in the optical domain with unprecedented certainty.
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Affiliation(s)
- Shuai Wang
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
| | - Shuai Liu
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
| | - Yilin Liu
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
| | - Shumin Xiao
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China.
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin, 150080, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, 030006, China.
| | - Zi Wang
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
| | - Yubin Fan
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
| | - Jiecai Han
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin, 150080, China
| | - Li Ge
- Department of Physics and Astronomy, College of Staten Island, CUNY, Staten Island, NY, 10314, USA.
- The Graduate Center, CUNY, New York, NY, 10016, USA.
| | - Qinghai Song
- Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, 030006, China.
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6
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Chen LK, Gu YZ, Cao QT, Gong Q, Wiersig J, Xiao YF. Regular-Orbit-Engineered Chaotic Photon Transport in Mixed Phase Space. PHYSICAL REVIEW LETTERS 2019; 123:173903. [PMID: 31702248 DOI: 10.1103/physrevlett.123.173903] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Revised: 08/20/2019] [Indexed: 06/10/2023]
Abstract
The dynamical evolution of light in asymmetric microcavities is of primary interest for broadband optical coupling and enhanced light-matter interaction. Here, we propose and demonstrate that the chaos-assisted photon transport can be engineered by regular periodic orbits in the momentum-position phase space of an asymmetric microcavity. Remarkably, light at different initial states experiences different evolution pathways, following either regular-chaotic channels or pure chaotic channels. Experimentally, we develop a nanofiber technique to accurately control the excitation position of light in the phase space. We find that the coupling to high-Q whispering gallery modes depends strongly on excitation in islands or chaotic sea, showing a good agreement with the theoretical prediction. The engineered chaotic photon transport has potential in light manipulation, broadband photonic devices, and phase-space reconstruction.
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Affiliation(s)
- Li-Kun Chen
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yu-Zhong Gu
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Qi-Tao Cao
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Qihuang Gong
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Jan Wiersig
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
| | - Yun-Feng Xiao
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
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7
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Fritzsch F, Ketzmerick R, Bäcker A. Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space. Phys Rev E 2019; 100:042219. [PMID: 31770964 DOI: 10.1103/physreve.100.042219] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Indexed: 11/07/2022]
Abstract
The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.
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Affiliation(s)
- Felix Fritzsch
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
| | - Roland Ketzmerick
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnd Bäcker
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
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8
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Firmbach M, Fritzsch F, Ketzmerick R, Bäcker A. Resonance-assisted tunneling in four-dimensional normal-form Hamiltonians. Phys Rev E 2019; 99:042213. [PMID: 31108719 DOI: 10.1103/physreve.99.042213] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Indexed: 11/07/2022]
Abstract
Nonlinear resonances in the classical phase space lead to a significant enhancement of tunneling. We demonstrate that the double resonance gives rise to a complicated tunneling peak structure. Such double resonances occur in Hamiltonian systems with an at least four-dimensional phase space. To explain the tunneling peak structure, we use the universal description of single and double resonances by the four-dimensional normal-form Hamiltonians. By applying perturbative methods, we reveal the underlying mechanism of enhancement and suppression of tunneling and obtain excellent quantitative agreement. Using a minimal matrix model, we obtain an intuitive understanding.
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Affiliation(s)
- Markus Firmbach
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Felix Fritzsch
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
| | - Roland Ketzmerick
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnd Bäcker
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.,Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
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9
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Yi CH, Kullig J, Wiersig J. Pair of Exceptional Points in a Microdisk Cavity under an Extremely Weak Deformation. PHYSICAL REVIEW LETTERS 2018; 120:093902. [PMID: 29547306 DOI: 10.1103/physrevlett.120.093902] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Indexed: 06/08/2023]
Abstract
One of the interesting features of open quantum and wave systems is the non-Hermitian degeneracy called an exceptional point, where not only energy levels but also the corresponding eigenstates coalesce. We demonstrate that such a degeneracy can appear in optical microdisk cavities by deforming the boundary extremely weakly. This surprising finding is explained by a semiclassical theory of dynamical tunneling. It is shown that the exceptional points come in nearly degenerated pairs, originating from the different symmetry classes of modes. A spatially local chirality of modes at the exceptional point is related to vortex structures of the Poynting vector.
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Affiliation(s)
- Chang-Hwan Yi
- Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
| | - Julius Kullig
- Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
- Institut für Physik, Technische Universität Ilmenau, D-98693 Ilmenau, Germany
| | - Jan Wiersig
- Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
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10
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Fritzsch F, Bäcker A, Ketzmerick R, Mertig N. Complex-path prediction of resonance-assisted tunneling in mixed systems. Phys Rev E 2017; 95:020202. [PMID: 28297952 DOI: 10.1103/physreve.95.020202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Indexed: 06/06/2023]
Abstract
We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a prediction based on just a few properties of the classical phase space. For the standard map excellent agreement with numerically determined tunneling rates is observed. The results should similarly apply to ionization rates and quality factors.
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Affiliation(s)
- Felix Fritzsch
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnd Bäcker
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Roland Ketzmerick
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Normann Mertig
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji 192-0397, Japan
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11
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Revuelta F, Vergini E, Benito RM, Borondo F. Semiclassical basis sets for the computation of molecular vibrational states. J Chem Phys 2017; 146:014107. [PMID: 28063420 DOI: 10.1063/1.4973376] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
In this paper, we extend a method recently reported [F. Revuelta et al., Phys. Rev. E 87, 042921 (2013)] for the calculation of the eigenstates of classically highly chaotic systems to cases of mixed dynamics, i.e., those presenting regular and irregular motions at the same energy. The efficiency of the method, which is based on the use of a semiclassical basis set of localized wave functions, is demonstrated by applying it to the determination of the vibrational states of a realistic molecular system, namely, the LiCN molecule.
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Affiliation(s)
- F Revuelta
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain
| | - E Vergini
- Departamento de Física, Comisión Nacional de Energía Atómica, Av. del Libertador 8250, 1429 Buenos Aires, Argentina
| | - R M Benito
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain
| | - F Borondo
- Instituto de Ciencias Matemáticas (ICMAT), 28049 Cantoblanco, Madrid, Spain
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12
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Mertig N, Kullig J, Löbner C, Bäcker A, Ketzmerick R. Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems. Phys Rev E 2016; 94:062220. [PMID: 28085465 DOI: 10.1103/physreve.94.062220] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Indexed: 06/06/2023]
Abstract
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling in a nonperturbative way. This provides the foundation for future semiclassical complex-path evaluations of resonance-assisted regular-to-chaotic tunneling. Our approach is based on a new class of integrable approximations which mimic the regular phase-space region and its dominant nonlinear resonance chain in a mixed regular-chaotic system. We illustrate the method for the standard map.
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Affiliation(s)
- Normann Mertig
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji 192-0397, Japan
| | - Julius Kullig
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany
| | - Clemens Löbner
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnd Bäcker
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Roland Ketzmerick
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
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13
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Kullig J, Wiersig J. Q spoiling in deformed optical microdisks due to resonance-assisted tunneling. Phys Rev E 2016; 94:022202. [PMID: 27627293 DOI: 10.1103/physreve.94.022202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2016] [Indexed: 06/06/2023]
Abstract
A recent experiment by Kwak et al. [Sci. Rep. 5, 9010 (2015)10.1038/srep09010] demonstrated the relevance of resonance-assisted tunneling for optical microcavities where resonance chains emerge in phase space due to boundary deformations. In this paper we adapt the perturbative description of resonance-assisted tunneling to calculate optical modes and the imaginary part of their complex wavenumber which determines the lifetime of the mode. We demonstrate our method at three example cavity shapes and compare our results to numerical data and perturbation theory for weakly deformed microdisk cavities.
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Affiliation(s)
- Julius Kullig
- Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
| | - Jan Wiersig
- Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
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14
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Revuelta F, Vergini E, Benito RM, Borondo F. Scar Functions, Barriers for Chemical Reactivity, and Vibrational Basis Sets. J Phys Chem A 2016; 120:4928-38. [DOI: 10.1021/acs.jpca.5b12541] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- F. Revuelta
- Grupo
de Sistemas Complejos, Escuela Técnica Superior de Ingeniería
Agronómica, Agroambiental y de Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain
- Instituto
de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain
| | - E. Vergini
- Departamento
de Física, Comisión Nacional de la Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina
| | - R. M. Benito
- Grupo
de Sistemas Complejos, Escuela Técnica Superior de Ingeniería
Agronómica, Agroambiental y de Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain
| | - F. Borondo
- Instituto
de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain
- Departamento
de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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15
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Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation. Sci Rep 2016; 6:19805. [PMID: 26803911 PMCID: PMC4726443 DOI: 10.1038/srep19805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2015] [Accepted: 12/11/2015] [Indexed: 11/10/2022] Open
Abstract
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory.
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Wisniacki DA, Schlagheck P. Quantum manifestations of classical nonlinear resonances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062923. [PMID: 26764790 DOI: 10.1103/physreve.92.062923] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2015] [Indexed: 06/05/2023]
Abstract
When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties.
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Affiliation(s)
- Diego A Wisniacki
- Departamento de Física and IFIBA, FCEyN, UBA Ciudad Universitaria, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Peter Schlagheck
- Departement de Physique, University of Liege, 4000 Liège, Belgium
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Gehler S, Löck S, Shinohara S, Bäcker A, Ketzmerick R, Kuhl U, Stöckmann HJ. Experimental Observation of Resonance-Assisted Tunneling. PHYSICAL REVIEW LETTERS 2015; 115:104101. [PMID: 26382678 DOI: 10.1103/physrevlett.115.104101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2015] [Indexed: 06/05/2023]
Abstract
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.
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Affiliation(s)
- Stefan Gehler
- Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany
- Department of Energy Management and Power System Operation, University of Kassel, D-34121 Kassel, Germany
| | - Steffen Löck
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- OncoRay, National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, Helmholtz-Zentrum Dresden-Rossendorf, Fetscherstraß e 74, PF 41, 01307 Dresden, Germany
| | - Susumu Shinohara
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnd Bäcker
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Roland Ketzmerick
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Ulrich Kuhl
- Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany
- Université Nice Sophia Antipolis, CNRS, Laboratoire de Physique de la Matière Condensée, UMR 7336 Parc Valrose, 06100 Nice, France
| | - Hans-Jürgen Stöckmann
- Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany
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