1
|
Betzold S, Düreth J, Dusel M, Emmerling M, Bieganowska A, Ohmer J, Fischer U, Höfling S, Klembt S. Dirac Cones and Room Temperature Polariton Lasing Evidenced in an Organic Honeycomb Lattice. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024; 11:e2400672. [PMID: 38605674 DOI: 10.1002/advs.202400672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Revised: 03/24/2024] [Indexed: 04/13/2024]
Abstract
Artificial 1D and 2D lattices have emerged as a powerful platform for the emulation of lattice Hamiltonians, the fundamental study of collective many-body effects, and phenomena arising from non-trivial topology. Exciton-polaritons, bosonic part-light and part-matter quasiparticles, combine pronounced nonlinearities with the possibility of on-chip implementation. In this context, organic semiconductors embedded in microcavities have proven to be versatile candidates to study nonlinear many-body physics and bosonic condensation, and in contrast to most inorganic systems, they allow the use at ambient conditions since they host ultra-stable Frenkel excitons. A well-controlled, high-quality optical lattice is implemented that accommodates light-matter quasiparticles. The realized polariton graphene presents with excellent cavity quality factors, showing distinct signatures of Dirac cone and flatband dispersions as well as polariton lasing at room temperature. This is realized by filling coupled dielectric microcavities with the fluorescent protein mCherry. The emergence of a coherent polariton condensate at ambient conditions are demonstrated, taking advantage of coupling conditions as precise and controllable as in state-of-the-art inorganic semiconductor-based systems, without the limitations of e.g. lattice matching in epitaxial growth. This progress allows straightforward extension to more complex systems, such as the study of topological phenomena in 2D lattices including topological lasers and non-Hermitian optics.
Collapse
Affiliation(s)
- Simon Betzold
- Lehrstuhl für Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Johannes Düreth
- Lehrstuhl für Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Marco Dusel
- Lehrstuhl für Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Monika Emmerling
- Lehrstuhl für Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Antonina Bieganowska
- Department of Experimental Physics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wyb. Wyspiańskiego 27, Wroclaw, 50-370, Poland
| | - Jürgen Ohmer
- Department of Biochemistry, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Utz Fischer
- Department of Biochemistry, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Sven Höfling
- Lehrstuhl für Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Sebastian Klembt
- Lehrstuhl für Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| |
Collapse
|
2
|
Xiong Z, Wu H, Cai Y, Zhai X, Liu T, Li B, Song T, Guo L, Liu Z, Dong Y, Liu P, Ren Y. Selective Excitation of Exciton-Polariton Condensate Modes in an Annular Perovskite Microcavity. NANO LETTERS 2024; 24. [PMID: 38620069 PMCID: PMC11057030 DOI: 10.1021/acs.nanolett.4c00634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2024] [Revised: 04/09/2024] [Accepted: 04/10/2024] [Indexed: 04/17/2024]
Abstract
Exciton-polariton systems composed of a light-matter quasi-particle with a light effective mass easily realize Bose-Einstein condensation. In this work, we constructed an annular trap in a halide perovskite semiconductor microcavity and observed the spontaneous formation of symmetrical petal-shaped exciton-polariton condensation in the annular trap at room temperature. In our study, we found that the number of petals of the petal-shaped exciton-polariton condensates, which is decided by the orbital angular momentum, is dependent on the light intensity distribution. Therefore, the selective excitation of perovskite microcavity exciton-polariton condensates under all-optical control can be realized by adjusting the light intensity distribution. This could pave the way to room-temperature topological devices, optical cryptographical devices, and new quantum gyroscopes in the exciton-polariton system.
Collapse
Affiliation(s)
- Zhenyu Xiong
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
| | - Hao Wu
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
- Lab
of Quantum Detection & Awareness, Space
Engineering University, Beijing 101416, China
| | - Yuanwen Cai
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
| | - Xiaokun Zhai
- Institute
of Molecular Plus, Tianjin University, Tianjin 300072, China
| | - Tong Liu
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
| | - Baili Li
- Lab
of Quantum Detection & Awareness, Space
Engineering University, Beijing 101416, China
| | - Tieling Song
- Lab
of Quantum Detection & Awareness, Space
Engineering University, Beijing 101416, China
| | - Longfei Guo
- Lab
of Quantum Detection & Awareness, Space
Engineering University, Beijing 101416, China
| | - Zhengliang Liu
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
| | - Yifan Dong
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
| | - Peicheng Liu
- Lab
of Quantum Detection & Awareness, Space
Engineering University, Beijing 101416, China
| | - Yuan Ren
- Department
of Aerospace Engineering and Technology, Space Engineering University, Beijing 101416, China
- Lab
of Quantum Detection & Awareness, Space
Engineering University, Beijing 101416, China
| |
Collapse
|
3
|
Yadav RK, Satapathy S, Deshmukh P, Datta B, Sharma A, Olsson AH, Chen J, Laursen BW, Flood AH, Sfeir MY, Menon VM. Direct Writing of Room Temperature Polariton Condensate Lattice. NANO LETTERS 2024. [PMID: 38598721 DOI: 10.1021/acs.nanolett.4c00586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
Realizing lattices of exciton polariton condensates has been of much interest owing to the potential of such systems to realize analogue Hamiltonian simulators and physical computing architectures. Here, we report the realization of a room temperature polariton condensate lattice using a direct-write approach. Polariton condensation is achieved in a microcavity embedded with host-guest Frenkel excitons of an organic dye (rhodamine) in a small-molecule ionic isolation lattice (SMILES). The microcavity is patterned using focused ion beam etching to realize arbitrary lattice geometries, including defect sites on demand. The band structure of the lattice and the emergence of condensation are imaged using momentum-resolved spectroscopy. The introduction of defect sites is shown to lower the condensation threshold and result in the formation of a defect band in the condensation spectrum. The present approach allows us to study periodic, quasiperiodic, and disordered polariton condensate lattices at room temperature using a direct-write approach.
Collapse
Affiliation(s)
- Ravindra Kumar Yadav
- Department of Physics, The City College of New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
| | - Sitakanta Satapathy
- Department of Physics, The City College of New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
| | - Prathmesh Deshmukh
- Department of Physics, The City College of New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
- The PhD Program in Physics, Graduate Center of the City University of New York, 365 5th Avenue, New York, New York 10016, United States
| | - Biswajit Datta
- Department of Physics, The City College of New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
| | - Addhyaya Sharma
- Department of Physics, The City College of New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
| | - Andrew H Olsson
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Junsheng Chen
- Nano-Science Center and Department of Chemistry, University of Copenhagen, Copenhagen 2100, Denmark
| | - Bo W Laursen
- Nano-Science Center and Department of Chemistry, University of Copenhagen, Copenhagen 2100, Denmark
| | - Amar H Flood
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Matthew Y Sfeir
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
| | - Vinod M Menon
- Department of Physics, The City College of New York, 85 St. Nicholas Terrace, New York, New York 10031, United States
- The PhD Program in Physics, Graduate Center of the City University of New York, 365 5th Avenue, New York, New York 10016, United States
| |
Collapse
|
4
|
Li X, Lubbers N, Tretiak S, Barros K, Zhang Y. Machine Learning Framework for Modeling Exciton Polaritons in Molecular Materials. J Chem Theory Comput 2024; 20:891-901. [PMID: 38168674 DOI: 10.1021/acs.jctc.3c01068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
A light-matter hybrid quasiparticle, called a polariton, is formed when molecules are strongly coupled to an optical cavity. Recent experiments have shown that polariton chemistry can manipulate chemical reactions. Polariton chemistry is a collective phenomenon, and its effects increase with the number of molecules in a cavity. However, simulating an ensemble of molecules in the excited state coupled to a cavity mode is theoretically and computationally challenging. Recent advances in machine learning (ML) techniques have shown promising capabilities in modeling ground-state chemical systems. This work presents a general protocol to predict excited-state properties, such as energies, transition dipoles, and nonadiabatic coupling vectors with the hierarchically interacting particle neural network. ML predictions are then applied to compute the potential energy surfaces and electronic spectra of a prototype azomethane molecule in the collective coupling scenario. These computational tools provide a much-needed framework to model and understand many molecules' emerging excited-state polariton chemistry.
Collapse
Affiliation(s)
- Xinyang Li
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Nicholas Lubbers
- Information Sciences, Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Kipton Barros
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Yu Zhang
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| |
Collapse
|
5
|
Kang H, Ma J, Li J, Zhang X, Liu X. Exciton Polaritons in Emergent Two-Dimensional Semiconductors. ACS NANO 2023; 17:24449-24467. [PMID: 38051774 DOI: 10.1021/acsnano.3c07993] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
The "marriage" of light (i.e., photon) and matter (i.e., exciton) in semiconductors leads to the formation of hybrid quasiparticles called exciton polaritons with fascinating quantum phenomena such as Bose-Einstein condensation (BEC) and photon blockade. The research of exciton polaritons has been evolving into an era with emergent two-dimensional (2D) semiconductors and photonic structures for their tremendous potential to break the current limitations of quantum fundamental study and photonic applications. In this Perspective, the basic concepts of 2D excitons, optical resonators, and the strong coupling regime are introduced. The research progress of exciton polaritons is reviewed, and important discoveries (especially the recent ones of 2D exciton polaritons) are highlighted. Subsequently, the emergent 2D exciton polaritons are discussed in detail, ranging from the realization of the strong coupling regime in various photonic systems to the discoveries of attractive phenomena with interesting physics and extensive applications. Moreover, emerging 2D semiconductors, such as 2D perovskites (2DPK) and 2D antiferromagnetic (AFM) semiconductors, are surveyed for the manipulation of exciton polaritons with distinct control degrees of freedom (DOFs). Finally, the outlook on the 2D exciton polaritons and their nonlinear interactions is presented with our initial numerical simulations. This Perspective not only aims to provide an in-depth overview of the latest fundamental findings in 2D exciton polaritons but also attempts to serve as a valuable resource to prospect explorations of quantum optics and topological photonic applications.
Collapse
Affiliation(s)
- Haifeng Kang
- Key Laboratory of Artificial Micro/Nano Structure of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan, 430072, P. R. China
| | - Jingwen Ma
- Faculty of Science and Engineering, The University of Hong Kong, Hong Kong, SAR, P. R. China
| | - Junyu Li
- Key Laboratory of Artificial Micro/Nano Structure of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan, 430072, P. R. China
| | - Xiang Zhang
- Faculty of Science and Engineering, The University of Hong Kong, Hong Kong, SAR, P. R. China
- Department of Physics, The University of Hong Kong, Hong Kong, SAR, P. R. China
| | - Xiaoze Liu
- Key Laboratory of Artificial Micro/Nano Structure of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan, 430072, P. R. China
- Wuhan Institute of Quantum Technology, Wuhan, 430206, P. R. China
- Wuhan University Shenzhen Research Institute, Shenzhen, 518057, P. R. China
| |
Collapse
|
6
|
Weight BM, Li X, Zhang Y. Theory and modeling of light-matter interactions in chemistry: current and future. Phys Chem Chem Phys 2023; 25:31554-31577. [PMID: 37842818 DOI: 10.1039/d3cp01415k] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
Light-matter interaction not only plays an instrumental role in characterizing materials' properties via various spectroscopic techniques but also provides a general strategy to manipulate material properties via the design of novel nanostructures. This perspective summarizes recent theoretical advances in modeling light-matter interactions in chemistry, mainly focusing on plasmon and polariton chemistry. The former utilizes the highly localized photon, plasmonic hot electrons, and local heat to drive chemical reactions. In contrast, polariton chemistry modifies the potential energy curvatures of bare electronic systems, and hence their chemistry, via forming light-matter hybrid states, so-called polaritons. The perspective starts with the basic background of light-matter interactions, molecular quantum electrodynamics theory, and the challenges of modeling light-matter interactions in chemistry. Then, the recent advances in modeling plasmon and polariton chemistry are described, and future directions toward multiscale simulations of light-matter interaction-mediated chemistry are discussed.
Collapse
Affiliation(s)
- Braden M Weight
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA
| | - Xinyang Li
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| |
Collapse
|
7
|
Ruggenthaler M, Sidler D, Rubio A. Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics. Chem Rev 2023; 123:11191-11229. [PMID: 37729114 PMCID: PMC10571044 DOI: 10.1021/acs.chemrev.2c00788] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Indexed: 09/22/2023]
Abstract
In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.
Collapse
Affiliation(s)
- Michael Ruggenthaler
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Dominik Sidler
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
| |
Collapse
|
8
|
Bhuyan R, Mony J, Kotov O, Castellanos GW, Gómez Rivas J, Shegai TO, Börjesson K. The Rise and Current Status of Polaritonic Photochemistry and Photophysics. Chem Rev 2023; 123:10877-10919. [PMID: 37683254 PMCID: PMC10540218 DOI: 10.1021/acs.chemrev.2c00895] [Citation(s) in RCA: 12] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Indexed: 09/10/2023]
Abstract
The interaction between molecular electronic transitions and electromagnetic fields can be enlarged to the point where distinct hybrid light-matter states, polaritons, emerge. The photonic contribution to these states results in increased complexity as well as an opening to modify the photophysics and photochemistry beyond what normally can be seen in organic molecules. It is today evident that polaritons offer opportunities for molecular photochemistry and photophysics, which has caused an ever-rising interest in the field. Focusing on the experimental landmarks, this review takes its reader from the advent of the field of polaritonic chemistry, over the split into polariton chemistry and photochemistry, to present day status within polaritonic photochemistry and photophysics. To introduce the field, the review starts with a general description of light-matter interactions, how to enhance these, and what characterizes the coupling strength. Then the photochemistry and photophysics of strongly coupled systems using Fabry-Perot and plasmonic cavities are described. This is followed by a description of room-temperature Bose-Einstein condensation/polariton lasing in polaritonic systems. The review ends with a discussion on the benefits, limitations, and future developments of strong exciton-photon coupling using organic molecules.
Collapse
Affiliation(s)
- Rahul Bhuyan
- Department
of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Göteborg, Sweden
| | - Jürgen Mony
- Department
of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Göteborg, Sweden
| | - Oleg Kotov
- Department
of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Gabriel W. Castellanos
- Department
of Applied Physics and Science Education, Eindhoven Hendrik Casimir
Institute and Institute for Complex Molecular Systems, Eindhoven University of Technology, 5612 AE Eindhoven, The Netherlands
| | - Jaime Gómez Rivas
- Department
of Applied Physics and Science Education, Eindhoven Hendrik Casimir
Institute and Institute for Complex Molecular Systems, Eindhoven University of Technology, 5612 AE Eindhoven, The Netherlands
| | - Timur O. Shegai
- Department
of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Karl Börjesson
- Department
of Chemistry and Molecular Biology, University
of Gothenburg, 412 96 Göteborg, Sweden
| |
Collapse
|
9
|
Wang G, Hou K, Liu Y, Bi H, Li W, Xue Y. Controllable bistability and squeezing of confined polariton dark solitons. OPTICS EXPRESS 2023; 31:22722-22732. [PMID: 37475376 DOI: 10.1364/oe.493274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 06/04/2023] [Indexed: 07/22/2023]
Abstract
The generation of squeezed light in semiconductor materials opens opportunities for building on-chip devices that are operated at the quantum level. Here we study theoretically a squeezed light source of polariton dark solitons confined in a geometric potential well of semiconductor microcavities in the strong coupling regime. We show that polariton dark solitons of odd and even parities can be created by tuning the potential depth. When driving the potential depth linearly, a bistability of solitons with the two different parities can be induced. Strong intensity squeezing is obtained near the turning point of the bistability due to the large nonlinear interaction, which can be controlled by the cavity detuning. The phase diagram of the bistability and squeezing of the dark solitons is obtained through large scale numerical calculations. Our study contributes to the current efforts in realizing topological excitations and squeezed light sources with solid-state devices.
Collapse
|
10
|
Wu J, Ghosh S, Gan Y, Shi Y, Mandal S, Sun H, Zhang B, Liew TCH, Su R, Xiong Q. Higher-order topological polariton corner state lasing. SCIENCE ADVANCES 2023; 9:eadg4322. [PMID: 37224247 DOI: 10.1126/sciadv.adg4322] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 04/20/2023] [Indexed: 05/26/2023]
Abstract
Unlike conventional laser, the topological laser is able to emit coherent light robustly against disorders and defects because of its nontrivial band topology. As a promising platform for low-power consumption, exciton polariton topological lasers require no population inversion, a unique property that can be attributed to the part-light-part-matter bosonic nature and strong nonlinearity of exciton polaritons. Recently, the discovery of higher-order topology has shifted the paradigm of topological physics to topological states at boundaries of boundaries, such as corners. However, such topological corner states have never been realized in the exciton polariton system yet. Here, on the basis of an extended two-dimensional Su-Schrieffer-Heeger lattice model, we experimentally demonstrate the topological corner states of perovskite polaritons and achieved polariton corner state lasing with a low threshold (approximately microjoule per square centimeter) at room temperature. The realization of such polariton corner states also provides a mechanism of polariton localization under topological protection, paving the way toward on-chip active polaritonics using higher-order topology.
Collapse
Affiliation(s)
- Jinqi Wu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Sanjib Ghosh
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
| | - Yusong Gan
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ying Shi
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Subhaskar Mandal
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Handong Sun
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Timothy C H Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
| | - Rui Su
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
- School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
| | - Qihua Xiong
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, P.R. China
- Collaborative Innovation Center of Quantum Matter, Beijing, P.R. China
| |
Collapse
|
11
|
Optically trapped room temperature polariton condensate in an organic semiconductor. Nat Commun 2022; 13:7191. [PMID: 36424397 PMCID: PMC9691723 DOI: 10.1038/s41467-022-34440-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Accepted: 10/25/2022] [Indexed: 11/27/2022] Open
Abstract
The strong nonlinearities of exciton-polariton condensates in lattices make them suitable candidates for neuromorphic computing and physical simulations of complex problems. So far, all room temperature polariton condensate lattices have been achieved by nanoimprinting microcavities, which by nature lacks the crucial tunability required for realistic reconfigurable simulators. Here, we report the observation of a quantised oscillating nonlinear quantum fluid in 1D and 2D potentials in an organic microcavity at room temperature, achieved by an on-the-fly fully tuneable optical approach. Remarkably, the condensate is delocalised from the excitation region by macroscopic distances, leading both to longer coherence and a threshold one order of magnitude lower than that with a conventional Gaussian excitation profile. We observe different mode selection behaviour compared to inorganic materials, which highlights the anomalous scaling of blueshift with pump intensity and the presence of sizeable energy-relaxation mechanisms. Our work is a major step towards a fully tuneable polariton simulator at room temperature.
Collapse
|
12
|
Tao R, Peng K, Haeberlé L, Li Q, Jin D, Fleming GR, Kéna-Cohen S, Zhang X, Bao W. Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature. NATURE MATERIALS 2022; 21:761-766. [PMID: 35681064 DOI: 10.1038/s41563-022-01276-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
Exciton polaritons, the part-light and part-matter quasiparticles in semiconductor optical cavities, are promising for exploring Bose-Einstein condensation, non-equilibrium many-body physics and analogue simulation at elevated temperatures. However, a room-temperature polaritonic platform on par with the GaAs quantum wells grown by molecular beam epitaxy at low temperatures remains elusive. The operation of such a platform calls for long-lifetime, strongly interacting excitons in a stringent material system with large yet nanoscale-thin geometry and homogeneous properties. Here, we address this challenge by adopting a method based on the solution synthesis of excitonic halide perovskites grown under nanoconfinement. Such nanoconfinement growth facilitates the synthesis of smooth and homogeneous single-crystalline large crystals enabling the demonstration of XY Hamiltonian lattices with sizes up to 10 × 10. With this demonstration, we further establish perovskites as a promising platform for room temperature polaritonic physics and pave the way for the realization of robust mode-disorder-free polaritonic devices at room temperature.
Collapse
Affiliation(s)
- Renjie Tao
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, USA
| | - Kai Peng
- Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Louis Haeberlé
- Department of Engineering Physics, École Polytechnique de Montréal, Montréal, Quebec, Canada
| | - Quanwei Li
- Department of Chemistry, University of California, Berkeley, CA, USA
| | - Dafei Jin
- Center for Nanoscale Materials, Argonne National Laboratory, Lemont, IL, USA
| | - Graham R Fleming
- Department of Chemistry, University of California, Berkeley, CA, USA
| | - Stéphane Kéna-Cohen
- Department of Engineering Physics, École Polytechnique de Montréal, Montréal, Quebec, Canada
| | - Xiang Zhang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, USA.
- Faculty of Science and Faculty of Engineering, The University of Hong Kong, Hong Kong, China.
| | - Wei Bao
- Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA.
| |
Collapse
|
13
|
Polariton Bose-Einstein condensate from a bound state in the continuum. Nature 2022; 605:447-452. [PMID: 35585343 DOI: 10.1038/s41586-022-04583-7] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 02/25/2022] [Indexed: 11/08/2022]
Abstract
Bound states in the continuum (BICs)1-3 are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone4. These BICs possess an invariant topological charge given by the winding number of the polarization vectors5, similar to vortices in quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not yet been fully exploited. Here we show non-equilibrium Bose-Einstein condensation of polaritons-hybrid light-matter excitations-occurring in a BIC thanks to its peculiar non-radiative nature, which favours polariton accumulation. The combination of the ultralong BIC lifetime and the tight confinement of the waveguide geometry enables the achievement of an extremely low threshold density for condensation, which is reached not in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we reveal ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light-matter optical circuits.
Collapse
|
14
|
Tian C, Chen L, Zhang Y, Zhu L, Hu W, Pan Y, Wang Z, Zhang F, Zhang L, Dong H, Zhou W. Relaxation Oscillations of an Exciton-Polariton Condensate Driven by Parametric Scattering. NANO LETTERS 2022; 22:3026-3032. [PMID: 35343702 DOI: 10.1021/acs.nanolett.2c00235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We report the observation of coherent oscillations in the relaxation dynamics of an exciton-polariton condensate that were driven by parametric scattering processes. As a result of the interbranch scattering scheme and the nonlinear polariton-polariton interactions, such parametric scatterings exhibit a high scattering efficiency that leads to the fast depletion of the polariton condensate and the periodic shut-off of the bosonic stimulation processes, eventually causing relaxation oscillations. Employing polariton-reservoir interactions, the oscillation dynamics in the time domain can be projected onto the energy space. In theory, our simulations using the open-dissipative Gross-Pitaevskii equation are in excellent agreement with experimental observations. Surprisingly, the oscillation patterns, including many excitation pulses, are clearly visible in our time-integrated images, implying the high stability of the relaxation oscillations driven by polariton parametric scatterings.
Collapse
Affiliation(s)
- Chuan Tian
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Linqi Chen
- Key Laboratory of Materials for High-Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Science, Shanghai 201800, China
| | - Yingjun Zhang
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
- Key Laboratory of Biomedical Engineering of Hainan Province, School of Biomedical Engineering, Hainan University, Haikou, Hainan 570100, China
| | - Liqing Zhu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Wenping Hu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Yichun Pan
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Zheng Wang
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Fangxin Zhang
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| | - Long Zhang
- Key Laboratory of Materials for High-Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Science, Shanghai 201800, China
- Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, Zhejiang 310024, China
| | - Hongxing Dong
- Key Laboratory of Materials for High-Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Science, Shanghai 201800, China
- Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, Zhejiang 310024, China
| | - Weihang Zhou
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
| |
Collapse
|
15
|
Satapathy S, Liu B, Deshmukh P, Molinaro PM, Dirnberger F, Khatoniar M, Koder RL, Menon VM. Thermalization of Fluorescent Protein Exciton-Polaritons at Room Temperature. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2109107. [PMID: 35165941 PMCID: PMC9022594 DOI: 10.1002/adma.202109107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Revised: 01/21/2022] [Indexed: 06/14/2023]
Abstract
Fluorescent proteins (FPs) have recently emerged as a serious contender for realizing ultralow threshold room temperature exciton-polariton condensation and lasing. This contribution investigates the thermalization of FP microcavity exciton-polaritons upon optical pumping under ambient conditions. Polariton cooling is realized using a new FP molecule, called mScarlet, coupled strongly to the optical modes in a Fabry-Pérot cavity. Interestingly, at the threshold excitation energy (fluence) of ≈9 nJ per pulse (15.6 mJ cm-2 ), an effective temperature is observed, Teff ≈ 350 ± 35 K close to the lattice temperature indicative of strongly thermalized exciton-polaritons at equilibrium. This efficient thermalization results from the interplay of radiative pumping facilitated by the energetics of the lower polariton branch and the cavity Q-factor. Direct evidence for dramatic switching from an equilibrium state into a metastable state is observed for the organic cavity polariton device at room temperature via deviation from the Maxwell-Boltzmann statistics at k‖ = 0 above the threshold. Thermalized polariton gases in organic systems at equilibrium hold substantial promise for designing room temperature polaritonic circuits, switches, and lattices for analog simulation.
Collapse
Affiliation(s)
- Sitakanta Satapathy
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
| | - Bin Liu
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, 48109, USA
| | - Prathmesh Deshmukh
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
- The PhD Program in Physics, The Graduate Center of the City University of New York, 365 5th Ave, New York, NY, 10016, USA
| | - Paul M Molinaro
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
| | - Florian Dirnberger
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
| | - Mandeep Khatoniar
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
- The PhD Program in Physics, The Graduate Center of the City University of New York, 365 5th Ave, New York, NY, 10016, USA
| | - Ronald L Koder
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
| | - Vinod M Menon
- Department of Physics, Center for Discovery and Innovation, The City College of New York, 85 St. Nicholas Terrace, New York, NY, 10031, USA
- The PhD Program in Physics, The Graduate Center of the City University of New York, 365 5th Ave, New York, NY, 10016, USA
| |
Collapse
|
16
|
Wang F, Liang F, Liu W, Fu Y, Lu D, Zhang G, Wang J, Yu H, Zhang H, Wu Y. Anion-Centered Polyhedron Strategy for Strengthening Photon Emission Induced by Electron-Phonon Coupling. Inorg Chem 2022; 61:4071-4079. [PMID: 35188388 DOI: 10.1021/acs.inorgchem.1c03875] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Electron-phonon coupling emerges as a growing frontier in the heart of condensed matter from physical symmetry to the electronic quantum state, but its quantitative strength dependence on the chemical structure has not been assessed. Here, we originally proposed the anion-centered polyhedron (ACP) strategy for elaborating the electron-phonon coupling interaction in rare-earth (RE) materials comprising three chemical factors, RE-O bond length, the effective charge of the coordinated atom, and structural dimensionality. Using Gd3+ cation with 4f7 configuration as a fluorescence probe, we found that the "free-O"-centered polyhedron is the most crucial motif in strengthening the phonon-assisted energy transfer and photon emission. The temperature-dependent Huang-Rhys S factors were calculated to identify the electron-phonon coupling intensity based on the fluorescence spectrum quantitatively. Finally, beyond conventional wisdom, a series of structural criteria were presented, serving as useful guidelines for discovering strongly coupled rare-earth optical materials. Our study breaks the long-time "blind"-searching diagram and provides reliable principles for many functional materials associated with electron-phonon coupling, such as superconductors, multiferroics, and phosphors.
Collapse
Affiliation(s)
- Fangyan Wang
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Fei Liang
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Wang Liu
- Key Lab Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Yu Fu
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Dazhi Lu
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Guochun Zhang
- Key Lab Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Jiyang Wang
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Haohai Yu
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Huaijin Zhang
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| | - Yicheng Wu
- State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
| |
Collapse
|
17
|
Jiang Z, Ren A, Yan Y, Yao J, Zhao YS. Exciton-Polaritons and Their Bose-Einstein Condensates in Organic Semiconductor Microcavities. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2106095. [PMID: 34881466 DOI: 10.1002/adma.202106095] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Revised: 09/22/2021] [Indexed: 06/13/2023]
Abstract
Exciton-polaritons are half-light, half-matter bosonic quasiparticles formed by strong exciton-photon coupling in semiconductor microcavities. These hybrid particles possess the strong nonlinear interactions of excitons and keep most of the characteristics of the underlying photons. As bosons, above a threshold density they can undergo Bose-Einstein condensation to a polariton condensate phase and exhibit a rich variety of exotic macroscopic quantum phenomena in solids. Recently, organic semiconductors have been considered as a promising material platform for these studies due to their room-temperature stability, good processability, and abundant photophysics and photochemistry. Herein, recent advances of exciton-polaritons and their Bose-Einstein condensates in organic semiconductor microcavities are summarized. First, the basic physics is introduced, and then their emerging applications are highlighted. The remaining questions are also discussed and a personal viewpoint about the potential directions for future research is given.
Collapse
Affiliation(s)
- Zhengjun Jiang
- Key Laboratory of Photochemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Ang Ren
- Key Laboratory of Photochemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Yongli Yan
- Key Laboratory of Photochemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
| | - Jiannian Yao
- Key Laboratory of Photochemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Yong Sheng Zhao
- Key Laboratory of Photochemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| |
Collapse
|
18
|
Su R, Estrecho E, Biegańska D, Huang Y, Wurdack M, Pieczarka M, Truscott AG, Liew TCH, Ostrovskaya EA, Xiong Q. Direct measurement of a non-Hermitian topological invariant in a hybrid light-matter system. SCIENCE ADVANCES 2021; 7:eabj8905. [PMID: 34731010 PMCID: PMC8565900 DOI: 10.1126/sciadv.abj8905] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Accepted: 09/13/2021] [Indexed: 05/31/2023]
Abstract
Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterized by topological invariants. In energy-conserving (Hermitian) systems, these invariants are determined by the winding of eigenstates in momentum space. In non-Hermitian systems, a topological invariant is predicted to emerge from the winding of the complex eigenenergies. Here, we directly measure the non-Hermitian topological invariant arising from exceptional points in the momentum-resolved spectrum of exciton polaritons. These are hybrid light-matter quasiparticles formed by photons strongly coupled to electron-hole pairs (excitons) in a halide perovskite semiconductor at room temperature. We experimentally map out both the real (energy) and imaginary (linewidth) parts of the spectrum near the exceptional points and extract the novel topological invariant—fractional spectral winding. Our work represents an essential step toward realization of non-Hermitian topological phases in a condensed matter system.
Collapse
Affiliation(s)
- Rui Su
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Eliezer Estrecho
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Dąbrówka Biegańska
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
- Department of Experimental Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Yuqing Huang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Matthias Wurdack
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Maciej Pieczarka
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
- Department of Experimental Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Andrew G. Truscott
- Laser Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Timothy C. H. Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore, Singapore
| | - Elena A. Ostrovskaya
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Qihua Xiong
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, P.R. China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
- Beijing Innovation Center for Future Chips, Tsinghua University, Beijing 100084, P.R. China
| |
Collapse
|
19
|
Motional narrowing, ballistic transport, and trapping of room-temperature exciton polaritons in an atomically-thin semiconductor. Nat Commun 2021; 12:5366. [PMID: 34508084 PMCID: PMC8433169 DOI: 10.1038/s41467-021-25656-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2021] [Accepted: 08/18/2021] [Indexed: 02/08/2023] Open
Abstract
Monolayer transition metal dichalcogenide crystals (TMDCs) hold great promise for semiconductor optoelectronics because their bound electron-hole pairs (excitons) are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, excitons can hybridise with cavity photons to form exciton polaritons, which inherit useful properties from their constituents. The ability to manipulate and trap polaritons on a microchip is critical for applications. Here, we create a non-trivial potential landscape for polaritons in monolayer WS2, and demonstrate their trapping and ballistic propagation across tens of micrometers. We show that the effects of dielectric disorder, which restrict the diffusion of WS2 excitons and broaden their spectral resonance, are dramatically reduced for polaritons, leading to motional narrowing and preserved partial coherence. Linewidth narrowing and coherence are further enhanced in the trap. Our results demonstrate the possibility of long-range dissipationless transport and efficient trapping of TMDC polaritons in ambient conditions.
Collapse
|
20
|
Anantharaman SB, Jo K, Jariwala D. Exciton-Photonics: From Fundamental Science to Applications. ACS NANO 2021; 15:12628-12654. [PMID: 34310122 DOI: 10.1021/acsnano.1c02204] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Semiconductors in all dimensionalities ranging from 0D quantum dots and molecules to 3D bulk crystals support bound electron-hole pair quasiparticles termed excitons. Over the past two decades, the emergence of a variety of low-dimensional semiconductors that support excitons combined with advances in nano-optics and photonics has burgeoned an advanced area of research that focuses on engineering, imaging, and modulating the coupling between excitons and photons, resulting in the formation of hybrid quasiparticles termed exciton-polaritons. This advanced area has the potential to bring about a paradigm shift in quantum optics, as well as classical optoelectronic devices. Here, we present a review on the coupling of light in excitonic semiconductors and previous investigations of the optical properties of these hybrid quasiparticles via both far-field and near-field imaging and spectroscopy techniques. Special emphasis is given to recent advances with critical evaluation of the bottlenecks that plague various materials toward practical device implementations including quantum light sources. Our review highlights a growing need for excitonic material development together with optical engineering and imaging techniques to harness the utility of excitons and their host materials for a variety of applications.
Collapse
Affiliation(s)
- Surendra B Anantharaman
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Kiyoung Jo
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Deep Jariwala
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| |
Collapse
|
21
|
Lackner L, Dusel M, Egorov OA, Han B, Knopf H, Eilenberger F, Schröder S, Watanabe K, Taniguchi T, Tongay S, Anton-Solanas C, Höfling S, Schneider C. Tunable exciton-polaritons emerging from WS 2 monolayer excitons in a photonic lattice at room temperature. Nat Commun 2021; 12:4933. [PMID: 34400620 PMCID: PMC8368091 DOI: 10.1038/s41467-021-24925-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 07/01/2021] [Indexed: 11/30/2022] Open
Abstract
Engineering non-linear hybrid light-matter states in tailored lattices is a central research strategy for the simulation of complex Hamiltonians. Excitons in atomically thin crystals are an ideal active medium for such purposes, since they couple strongly with light and bear the potential to harness giant non-linearities and interactions while presenting a simple sample-processing and room temperature operability. We demonstrate lattice polaritons, based on an open, high-quality optical cavity, with an imprinted photonic lattice strongly coupled to excitons in a WS2 monolayer. We experimentally observe the emergence of the canonical band-structure of particles in a one-dimensional lattice at room temperature, and demonstrate frequency reconfigurability over a spectral window exceeding 85 meV, as well as the systematic variation of the nearest-neighbour coupling, reflected by a tunability in the bandwidth of the p-band polaritons by 7 meV. The technology presented in this work is a critical demonstration towards reconfigurable photonic emulators operated with non-linear photonic fluids, offering a simple experimental implementation and working at ambient conditions.
Collapse
Affiliation(s)
- L Lackner
- Technische Physik and Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Universität Würzburg, Würzburg, Germany.
- Institute of Physics, University of Oldenburg, Oldenburg, Germany.
| | - M Dusel
- Technische Physik and Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Universität Würzburg, Würzburg, Germany
| | - O A Egorov
- Institute of Condensed Matter Theory and Solid State Optics, Friedrich Schiller University, Jena, Germany
| | - B Han
- Institute of Physics, University of Oldenburg, Oldenburg, Germany
| | - H Knopf
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University, Jena, Germany
- Fraunhofer-Institute for Applied Optics and Precision Engineering IOF, Jena, Germany
- Max Planck School of Photonics, Jena, Germany
| | - F Eilenberger
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University, Jena, Germany
- Fraunhofer-Institute for Applied Optics and Precision Engineering IOF, Jena, Germany
- Max Planck School of Photonics, Jena, Germany
| | - S Schröder
- Fraunhofer-Institute for Applied Optics and Precision Engineering IOF, Jena, Germany
| | - K Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - T Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - S Tongay
- School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, AZ, USA
| | - C Anton-Solanas
- Institute of Physics, University of Oldenburg, Oldenburg, Germany
| | - S Höfling
- Technische Physik and Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Universität Würzburg, Würzburg, Germany
| | - C Schneider
- Technische Physik and Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Universität Würzburg, Würzburg, Germany.
- Institute of Physics, University of Oldenburg, Oldenburg, Germany.
| |
Collapse
|
22
|
Dusel M, Betzold S, Harder TH, Emmerling M, Beierlein J, Ohmer J, Fischer U, Thomale R, Schneider C, Höfling S, Klembt S. Room-Temperature Topological Polariton Laser in an Organic Lattice. NANO LETTERS 2021; 21:6398-6405. [PMID: 34328737 DOI: 10.1021/acs.nanolett.1c00661] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Interacting bosonic particles in artificial lattices have proven to be a powerful tool for the investigation of exotic phases of matter as well as phenomena resulting from nontrivial topology. Exciton-polaritons, bosonic quasi-particles of light and matter, have been shown to combine the on-chip benefits of optical systems with strong interactions, inherited from their matter character. Technologically significant semiconductor platforms strictly require cryogenic temperatures. In this communication, we demonstrate exciton-polariton lasing for topological defects emerging from the imprinted lattice structure at room temperature. We utilize red fluorescent protein derived from DsRed of Discosoma sea anemones, hosting highly stable Frenkel excitons. Using a patterned mirror cavity, we tune the lattice potential landscape of a linear Su-Schrieffer-Heeger chain to design topological defects at domain boundaries and at the edge. We unequivocally demonstrate polariton lasing from these topological defects. This progress has paved the road to interacting boson many-body physics under ambient conditions.
Collapse
Affiliation(s)
| | | | | | | | | | | | | | | | | | - Sven Höfling
- SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY 16 9SS, United Kingdom
| | | |
Collapse
|
23
|
Mirek R, Opala A, Comaron P, Furman M, Król M, Tyszka K, Seredyński B, Ballarini D, Sanvitto D, Liew TCH, Pacuski W, Suffczyński J, Szczytko J, Matuszewski M, Piętka B. Neuromorphic Binarized Polariton Networks. NANO LETTERS 2021; 21:3715-3720. [PMID: 33635656 PMCID: PMC8155323 DOI: 10.1021/acs.nanolett.0c04696] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2020] [Revised: 02/23/2021] [Indexed: 06/12/2023]
Abstract
The rapid development of artificial neural networks and applied artificial intelligence has led to many applications. However, current software implementation of neural networks is severely limited in terms of performance and energy efficiency. It is believed that further progress requires the development of neuromorphic systems, in which hardware directly mimics the neuronal network structure of a human brain. Here, we propose theoretically and realize experimentally an optical network of nodes performing binary operations. The nonlinearity required for efficient computation is provided by semiconductor microcavities in the strong quantum light-matter coupling regime, which exhibit exciton-polariton interactions. We demonstrate the system performance against a pattern recognition task, obtaining accuracy on a par with state-of-the-art hardware implementations. Our work opens the way to ultrafast and energy-efficient neuromorphic systems taking advantage of ultrastrong optical nonlinearity of polaritons.
Collapse
Affiliation(s)
- Rafał Mirek
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Andrzej Opala
- Institute
of Physics, Polish Academy
of Sciences, Aleja Lotników
32/46, PL-02-668 Warsaw, Poland
| | - Paolo Comaron
- Institute
of Physics, Polish Academy
of Sciences, Aleja Lotników
32/46, PL-02-668 Warsaw, Poland
| | - Magdalena Furman
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Mateusz Król
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Krzysztof Tyszka
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Bartłomiej Seredyński
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Dario Ballarini
- CNR
NANOTEC−Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Daniele Sanvitto
- CNR
NANOTEC−Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Timothy C. H. Liew
- School
of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
| | - Wojciech Pacuski
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Jan Suffczyński
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Jacek Szczytko
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Michał Matuszewski
- Institute
of Physics, Polish Academy
of Sciences, Aleja Lotników
32/46, PL-02-668 Warsaw, Poland
| | - Barbara Piętka
- Institute
of Experimental Physics, Faculty of Physics,
University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| |
Collapse
|
24
|
Su R, Ghosh S, Liew TCH, Xiong Q. Optical switching of topological phase in a perovskite polariton lattice. SCIENCE ADVANCES 2021; 7:7/21/eabf8049. [PMID: 34020955 PMCID: PMC8139588 DOI: 10.1126/sciadv.abf8049] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 03/31/2021] [Indexed: 05/20/2023]
Abstract
Strong light-matter interaction enriches topological photonics by dressing light with matter, which provides the possibility to realize active nonlinear topological devices with immunity to defects. Topological exciton polaritons-half-light, half-matter quasiparticles with giant optical nonlinearity-represent a unique platform for active topological photonics. Previous demonstrations of exciton polariton topological insulators demand cryogenic temperatures, and their topological properties are usually fixed. Here, we experimentally demonstrate a room temperature exciton polariton topological insulator in a perovskite zigzag lattice. Polarization serves as a degree of freedom to switch between distinct topological phases, and the topologically nontrivial polariton edge states persist in the presence of onsite energy perturbations, showing strong immunity to disorder. We further demonstrate exciton polariton condensation into the topological edge states under optical pumping. These results provide an ideal platform for realizing active topological polaritonic devices working at ambient conditions, which can find important applications in topological lasers, optical modulation, and switching.
Collapse
Affiliation(s)
- Rui Su
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
| | - Sanjib Ghosh
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Timothy C H Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore 637371, Singapore
| | - Qihua Xiong
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, P.R. China.
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
| |
Collapse
|
25
|
Wang J, Xu H, Su R, Peng Y, Wu J, Liew TCH, Xiong Q. Spontaneously coherent orbital coupling of counterrotating exciton polaritons in annular perovskite microcavities. LIGHT, SCIENCE & APPLICATIONS 2021; 10:45. [PMID: 33649295 PMCID: PMC7921445 DOI: 10.1038/s41377-021-00478-w] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Revised: 01/04/2021] [Accepted: 01/19/2021] [Indexed: 05/26/2023]
Abstract
Exciton-polariton condensation is regarded as a spontaneous macroscopic quantum phenomenon with phase ordering and collective coherence. By engineering artificial annular potential landscapes in halide perovskite semiconductor microcavities, we experimentally and theoretically demonstrate the room-temperature spontaneous formation of a coherent superposition of exciton-polariton orbital states with symmetric petal-shaped patterns in real space, resulting from symmetry breaking due to the anisotropic effective potential of the birefringent perovskite crystals. The lobe numbers of such petal-shaped polariton condensates can be precisely controlled by tuning the annular potential geometry. These petal-shaped condensates form in multiple orbital states, carrying locked alternating π phase shifts and vortex-antivortex superposition cores, arising from the coupling of counterrotating exciton-polaritons in the confined circular waveguide. Our geometrically patterned microcavity exhibits promise for realizing room-temperature topological polaritonic devices and optical polaritonic switches based on periodic annular potentials.
Collapse
Affiliation(s)
- Jun Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Huawen Xu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Rui Su
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
| | - Yutian Peng
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, China
| | - Jinqi Wu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Timothy C H Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore, Singapore.
| | - Qihua Xiong
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, P.R. China.
| |
Collapse
|
26
|
Mandal S, Banerjee R, Ostrovskaya EA, Liew TCH. Nonreciprocal Transport of Exciton Polaritons in a Non-Hermitian Chain. PHYSICAL REVIEW LETTERS 2020; 125:123902. [PMID: 33016708 DOI: 10.1103/physrevlett.125.123902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
We consider exciton polaritons in a zigzag chain of coupled elliptical micropillars subjected to incoherent excitation. The driven-dissipative nature of the system along with the naturally present polarization splitting inside the pillars gives rise to nonreciprocal dynamics, which eventually leads to the non-Hermitian skin effect, where all the modes of the system collapse to one edge. As a result, the polaritons propagate only in one direction along the chain, independent of the excitation position, and the propagation in the opposite direction is suppressed. The system shows robustness against disorder and, using the bistable nature of polaritons to encode information, we show one-way information transfer. This paves the way for compact and robust feedback-free one-dimensional polariton transmission channels without the need for external magnetic field, which are compatible with proposals for polaritonic circuits.
Collapse
Affiliation(s)
- S Mandal
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - R Banerjee
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Elena A Ostrovskaya
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - T C H Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| |
Collapse
|
27
|
Ballarini D, Gianfrate A, Panico R, Opala A, Ghosh S, Dominici L, Ardizzone V, De Giorgi M, Lerario G, Gigli G, Liew TCH, Matuszewski M, Sanvitto D. Polaritonic Neuromorphic Computing Outperforms Linear Classifiers. NANO LETTERS 2020; 20:3506-3512. [PMID: 32251601 DOI: 10.1021/acs.nanolett.0c00435] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Machine learning software applications are ubiquitous in many fields of science and society for their outstanding capability to solve computationally vast problems like the recognition of patterns and regularities in big data sets. In spite of these impressive achievements, such processors are still based on the so-called von Neumann architecture, which is a bottleneck for faster and power-efficient neuromorphic computation. Therefore, one of the main goals of research is to conceive physical realizations of artificial neural networks capable of performing fully parallel and ultrafast operations. Here we show that lattices of exciton-polariton condensates accomplish neuromorphic computing with outstanding accuracy thanks to their high optical nonlinearity. We demonstrate that our neural network significantly increases the recognition efficiency compared with the linear classification algorithms on one of the most widely used benchmarks, the MNIST problem, showing a concrete advantage from the integration of optical systems in neural network architectures.
Collapse
Affiliation(s)
- Dario Ballarini
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Antonio Gianfrate
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Riccardo Panico
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Andrzej Opala
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, PL-02-668 Warsaw, Poland
| | - Sanjib Ghosh
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
| | - Lorenzo Dominici
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Vincenzo Ardizzone
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Milena De Giorgi
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Giovanni Lerario
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Giuseppe Gigli
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Timothy C H Liew
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
| | - Michal Matuszewski
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, PL-02-668 Warsaw, Poland
| | - Daniele Sanvitto
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| |
Collapse
|