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An invisible acoustic sensor based on parity-time symmetry. Nat Commun 2015; 6:5905. [DOI: 10.1038/ncomms6905] [Citation(s) in RCA: 438] [Impact Index Per Article: 48.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2014] [Accepted: 11/19/2014] [Indexed: 02/03/2023] Open
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Golshani M, Weimann S, Jafari K, Nezhad MK, Langari A, Bahrampour AR, Eichelkraut T, Mahdavi SM, Szameit A. Impact of loss on the wave dynamics in photonic waveguide lattices. PHYSICAL REVIEW LETTERS 2014; 113:123903. [PMID: 25279632 DOI: 10.1103/physrevlett.113.123903] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Indexed: 06/03/2023]
Abstract
We analyze the impact of loss in lattices of coupled optical waveguides and find that, in such a case, the hopping between adjacent waveguides is necessarily complex. This results not only in a transition of the light spreading from ballistic to diffusive, but also in a new kind of diffraction that is caused by loss dispersion. We prove our theoretical results with experimental observations.
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Affiliation(s)
- M Golshani
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran
| | - S Weimann
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Kh Jafari
- Department of Physics and Institute for Plasma Research, Kharazmi University, Tehran 15614, Iran
| | - M Khazaei Nezhad
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran
| | - A Langari
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran and Center of Excellence in Complex Systems and Condensed Matter (CSCM), Sharif University of Technology, Tehran 145888-9694, Iran and Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - A R Bahrampour
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran
| | - T Eichelkraut
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - S M Mahdavi
- Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran and Institute for Nanoscience and Nanotechnology, Sharif University of Technology, Tehran 89694-14588, Iran
| | - A Szameit
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
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Lawrence M, Xu N, Zhang X, Cong L, Han J, Zhang W, Zhang S. Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces. PHYSICAL REVIEW LETTERS 2014; 113:093901. [PMID: 25215984 DOI: 10.1103/physrevlett.113.093901] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2014] [Indexed: 05/17/2023]
Abstract
By utilizing the vector nature of light as well as the inherent anisotropy of artificial meta-atoms, we investigate parity time symmetry breaking in polarization space using a metasurface with anisotropic absorption, whose building blocks consist of two orthogonally orientated meta-atoms with the same resonant frequency but different loss coefficients. By varying their coupling strength, we directly observe a phase transition in the eigenpolarization states of the system, across which the long axis of the eigenpolarization ellipses experience a sudden rotation of 45°. Despite the lack of rotational symmetry of the metasurface, precisely at the phase transition, known as the exceptional point, the eigenmodes coalesce into a single circularly polarized state. The PT symmetric metasurfaces are experimentally implemented at terahertz frequencies.
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Affiliation(s)
- Mark Lawrence
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Ningning Xu
- School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
| | - Xueqian Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom and Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
| | - Longqing Cong
- Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
| | - Jiaguang Han
- Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
| | - Weili Zhang
- School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA and Center for Terahertz Waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
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Sun Y, Tan W, Li HQ, Li J, Chen H. Experimental demonstration of a coherent perfect absorber with PT phase transition. PHYSICAL REVIEW LETTERS 2014; 112:143903. [PMID: 24765965 DOI: 10.1103/physrevlett.112.143903] [Citation(s) in RCA: 125] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2013] [Indexed: 06/03/2023]
Abstract
We report the realization of a coherent perfect absorber, using a pair of passive resonators coupled to a microwave transmission line in the background, which can completely absorb light in its parity-time (PT-)symmetric phase but not in its broken phase. Instead of balancing material gain and loss, we exploit the incident waves in the open system as an effective gain so that ideal PT symmetry can be established by using only passive materials. Such a route will be effective to construct PT-symmetric metamaterials and also tunable PT-symmetric optical elements in general. It also provides a flexible platform for studying exceptional-point physics with both electric and magnetic responses.
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Affiliation(s)
- Yong Sun
- Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Wei Tan
- Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China and Beijing Computational Science Research Center, Beijing 100084, China
| | - Hong-qiang Li
- Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Jensen Li
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Hong Chen
- Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
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Bittner S, Dietz B, Harney HL, Miski-Oglu M, Richter A, Schäfer F. Scattering experiments with microwave billiards at an exceptional point under broken time-reversal invariance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032909. [PMID: 24730915 DOI: 10.1103/physreve.89.032909] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Indexed: 06/03/2023]
Abstract
Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be PT invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
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Affiliation(s)
- S Bittner
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany and Laboratoire de Photonique Quantique et Moléculaire, CNRS UMR 8537, Institut d'Alembert FR 3242, Ecole Normale Supérieure de Cachan, F-94235 Cachan, France
| | - B Dietz
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - H L Harney
- Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany
| | - M Miski-Oglu
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - A Richter
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - F Schäfer
- Division of Physics and Astronomy, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
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Luo X, Huang J, Zhong H, Qin X, Xie Q, Kivshar YS, Lee C. Pseudo-parity-time symmetry in optical systems. PHYSICAL REVIEW LETTERS 2013; 110:243902. [PMID: 25165925 DOI: 10.1103/physrevlett.110.243902] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2013] [Indexed: 06/03/2023]
Abstract
We introduce a novel concept of the pseudo-parity-time (pseudo-PT) symmetry in periodically modulated optical systems with balanced gain and loss. We demonstrate that whether or not the original system is PT symmetric, we can manipulate the property of the PT symmetry by applying a periodic modulation in such a way that the effective system derived by the high-frequency Floquet method is PT symmetric. If the original system is non-PT symmetric, the PT symmetry in the effective system will lead to quasistationary propagation that can be associated with the pseudo-PT symmetry. Our results provide a promising approach for manipulating the PT symmetry of realistic systems.
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Affiliation(s)
- Xiaobing Luo
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China and Department of Physics, Jinggangshan University, Ji'an 343009, China
| | - Jiahao Huang
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
| | - Honghua Zhong
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
| | - Xizhou Qin
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
| | - Qiongtao Xie
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China and Department of Physics and Key Laboratory of Low-Dimensional Quantum Structure and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081, China
| | - Yuri S Kivshar
- Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
| | - Chaohong Lee
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, China and Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
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Bender CM, Brody DC, Caldeira J, Günther U, Meister BK, Samsonov BF. PT-symmetric quantum state discrimination. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2013; 371:20120160. [PMID: 23509387 DOI: 10.1098/rsta.2012.0160] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The objective of this paper is to explain and elucidate the formalism of PT quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ(1)> or |ψ(2)>. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of PT quantum mechanics and the approach is based on the fact that a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states |ψ(1)> and |ψ(2)> are orthogonal. Using PT quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability p.
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Affiliation(s)
- Carl M Bender
- Department of Physics, King's College London, Strand, London WC2R 1LS, UK
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Bender CM, DeKieviet M, Klevansky SP. PT quantum mechanics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2013; 371:20120523. [PMID: 23509390 PMCID: PMC3638376 DOI: 10.1098/rsta.2012.0523] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
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Affiliation(s)
- Carl M Bender
- Department of Physics, Washington University, St. Louis, MO 63130, USA.
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Brody DC, Graefe EM. Mixed-state evolution in the presence of gain and loss. PHYSICAL REVIEW LETTERS 2012; 109:230405. [PMID: 23368172 DOI: 10.1103/physrevlett.109.230405] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2012] [Indexed: 06/01/2023]
Abstract
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.
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Affiliation(s)
- Dorje C Brody
- Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, United Kingdom
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Parity–time synthetic photonic lattices. Nature 2012; 488:167-71. [DOI: 10.1038/nature11298] [Citation(s) in RCA: 1347] [Impact Index Per Article: 112.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2012] [Accepted: 06/08/2012] [Indexed: 11/08/2022]
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