1
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Di Giulio V, Akerboom E, Polman A, García de Abajo FJ. Toward Optimum Coupling between Free Electrons and Confined Optical Modes. ACS NANO 2024; 18:14255-14275. [PMID: 38775711 PMCID: PMC11155252 DOI: 10.1021/acsnano.3c12977] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Revised: 04/10/2024] [Accepted: 04/25/2024] [Indexed: 06/05/2024]
Abstract
Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.
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Affiliation(s)
- Valerio Di Giulio
- The
Barcelona Institute of Science and Technology, Institut de Ciencies Fotoniques-ICFO, 08860 Castelldefels (Barcelona), Spain
| | - Evelijn Akerboom
- Center
for Nanophotonics, NWO-Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Albert Polman
- Center
for Nanophotonics, NWO-Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - F. Javier García de Abajo
- The
Barcelona Institute of Science and Technology, Institut de Ciencies Fotoniques-ICFO, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució
Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
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2
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Rasmussen TP, Echarri ÁR, Cox JD, de Abajo FJG. Generation of entangled waveguided photon pairs by free electrons. SCIENCE ADVANCES 2024; 10:eadn6312. [PMID: 38517969 DOI: 10.1126/sciadv.adn6312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/16/2024] [Indexed: 03/24/2024]
Abstract
Entangled photons are a key resource in quantum technologies. While intense laser light propagating in nonlinear crystals is conventionally used to generate entangled photons, such schemes have low efficiency due to the weak nonlinear response of known materials and losses associated with in/out photon coupling. Here, we show how to generate entangled polariton pairs directly within optical waveguides using free electrons. The measured energy loss of undeflected electrons heralds the production of counter-propagating polariton pairs entangled in energy and emission direction. For illustration, we study the excitation of plasmon polaritons in metal strip waveguides that strongly enhance light-matter interactions, rendering two-plasmon generation dominant over single-plasmon excitation. We demonstrate that electron energy losses detected within optimal frequency ranges can reliably signal the generation of plasmon pairs entangled in energy and momentum. Our proposed scheme is directly applicable to other types of optical waveguides for in situ generation of entangled photon pairs.
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Affiliation(s)
- Theis P Rasmussen
- POLIMA-Center for Polariton-driven Light-Matter Interactions, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Álvaro Rodríguez Echarri
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- Max-Born-Institut, 12489 Berlin, Germany
| | - Joel D Cox
- POLIMA-Center for Polariton-driven Light-Matter Interactions, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
- Danish Institute for Advanced Study, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - F Javier García de Abajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
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3
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Feist A, Huang G, Arend G, Yang Y, Henke JW, Raja AS, Jasmin Kappert F, Wang RN, Lourenço-Martins H, Qiu Z, Liu J, Kfir O, Kippenberg TJ, Ropers C. Electron-Photon Pairs Enable Contrast Enhanced Cavity Mode Imaging. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2023; 29:382-383. [PMID: 37613465 DOI: 10.1093/micmic/ozad067.180] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/25/2023]
Affiliation(s)
- Armin Feist
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
| | - Guanhao Huang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Germaine Arend
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
| | - Yujia Yang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Jan-Wilke Henke
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
| | - Arslan Sajid Raja
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - F Jasmin Kappert
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
| | - Rui Ning Wang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Hugo Lourenço-Martins
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
| | - Zheru Qiu
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Junqiu Liu
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Ofer Kfir
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
| | - Tobias J Kippenberg
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Claus Ropers
- Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- 4th Physical Institute - Solids and Nanostructures, University of Göttingen, Göttingen, Germany
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4
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Karnieli A, Fan S. Jaynes-Cummings interaction between low-energy free electrons and cavity photons. SCIENCE ADVANCES 2023; 9:eadh2425. [PMID: 37256955 PMCID: PMC10413651 DOI: 10.1126/sciadv.adh2425] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 04/21/2023] [Indexed: 06/02/2023]
Abstract
The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics; however, it relies on bound-electron emitters fundamentally limited by the binding Coulomb potential. In this work, we propose theoretically a new approach to realizing the Jaynes-Cummings model using low-energy free electrons coupled to dielectric microcavities and exemplify several quantum technologies made possible by this approach. Using quantum recoil, a large detuning inhibits the emission of multiple consecutive photons, effectively transforming the free electron into a few-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons, photon pairs, and even a quantum SWAP gate between a photon and a free electron, with unity efficiency and high fidelity. Tunable by their kinetic energy, quantum free electrons are inherently versatile emitters with an engineerable emission wavelength. Hence, they pave the way toward new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.
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Affiliation(s)
- Aviv Karnieli
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
| | - Shanhui Fan
- Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
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5
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Yang Y, Roques-Carmes C, Kooi SE, Tang H, Beroz J, Mazur E, Kaminer I, Joannopoulos JD, Soljačić M. Photonic flatband resonances for free-electron radiation. Nature 2023; 613:42-47. [PMID: 36600060 DOI: 10.1038/s41586-022-05387-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Accepted: 09/26/2022] [Indexed: 01/06/2023]
Abstract
Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation-diffractionless wavepacket propagation-in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith-Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light-electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.
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Affiliation(s)
- Yi Yang
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Physics, University of Hong Kong, Hong Kong, China.
| | - Charles Roques-Carmes
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Steven E Kooi
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Haoning Tang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Justin Beroz
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Eric Mazur
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Ido Kaminer
- Department of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Haifa, Israel
| | - John D Joannopoulos
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Marin Soljačić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, MA, USA
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6
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Di Giulio V, García de Abajo FJ. Optical-cavity mode squeezing by free electrons. NANOPHOTONICS 2022; 11:4659-4670. [PMID: 36482983 PMCID: PMC9709710 DOI: 10.1515/nanoph-2022-0481] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 09/24/2022] [Indexed: 06/17/2023]
Abstract
The generation of nonclassical light states bears a paramount importance in quantum optics and is largely relying on the interaction between intense laser pulses and nonlinear media. Recently, electron beams, such as those used in ultrafast electron microscopy to retrieve information from a specimen, have been proposed as a tool to manipulate both bright and dark confined optical excitations, inducing semiclassical states of light that range from coherent to thermal mixtures. Here, we show that the ponderomotive contribution to the electron-cavity interaction, which we argue to be significant for low-energy electrons subject to strongly confined near-fields, can actually create a more general set of optical states, including coherent and squeezed states. The postinteraction electron spectrum further reveals signatures of the nontrivial role played by A 2 terms in the light-matter coupling Hamiltonian, particularly when the cavity is previously excited by either chaotic or coherent illumination. Our work introduces a disruptive approach to the creation of nontrivial quantum cavity states for quantum information and optics applications, while it suggests unexplored possibilities for electron beam shaping.
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Affiliation(s)
- Valerio Di Giulio
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860Castelldefels, Barcelona, Spain
| | - F. Javier García de Abajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860Castelldefels, Barcelona, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010,Barcelona, Spain
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7
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Konečná A, Iyikanat F, García de Abajo FJ. Entangling free electrons and optical excitations. SCIENCE ADVANCES 2022; 8:eabo7853. [PMID: 36427323 PMCID: PMC9699672 DOI: 10.1126/sciadv.abo7853] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 10/07/2022] [Indexed: 05/30/2023]
Abstract
The inelastic interaction between flying particles and optical nanocavities gives rise to entangled states in which some excitations of the latter are paired with momentum changes in the former. Specifically, free-electron entanglement with nanocavity modes opens appealing opportunities associated with the strong interaction capabilities of the electrons. However, the achievable degree of entanglement is currently limited by the lack of control over the resulting state mixtures. Here, we propose a scheme to generate pure entanglement between designated optical-cavity excitations and separable free-electron states. We shape the electron wave function profile to select the accessible cavity modes and simultaneously associate them with targeted electron scattering directions. This concept is exemplified through theoretical calculations of free-electron entanglement with degenerate and nondegenerate plasmon modes in silver nanoparticles and atomic vibrations in an inorganic molecule. The generated entanglement can be further propagated through its electron component to extend quantum interactions beyond existing protocols.
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Affiliation(s)
- Andrea Konečná
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Central European Institute of Technology, Brno University of Technology, Brno 61200, Czech Republic
| | - Fadil Iyikanat
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - F. Javier García de Abajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
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8
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Feist A, Huang G, Arend G, Yang Y, Henke JW, Raja AS, Kappert FJ, Wang RN, Lourenço-Martins H, Qiu Z, Liu J, Kfir O, Kippenberg TJ, Ropers C. Cavity-mediated electron-photon pairs. Science 2022; 377:777-780. [PMID: 35951690 DOI: 10.1126/science.abo5037] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Quantum information, communication, and sensing rely on the generation and control of quantum correlations in complementary degrees of freedom. Free electrons coupled to photonics promise novel hybrid quantum technologies, although single-particle correlations and entanglement have yet to be shown. In this work, we demonstrate the preparation of electron-photon pair states using the phase-matched interaction of free electrons with the evanescent vacuum field of a photonic chip-based optical microresonator. Spontaneous inelastic scattering produces intracavity photons coincident with energy-shifted electrons, which we employ for noise-suppressed optical mode imaging. This parametric pair-state preparation will underpin the future development of free-electron quantum optics, providing a route to quantum-enhanced imaging, electron-photon entanglement, and heralded single-electron and Fock-state photon sources.
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Affiliation(s)
- Armin Feist
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
| | - Guanhao Huang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Germaine Arend
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
| | - Yujia Yang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jan-Wilke Henke
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
| | - Arslan Sajid Raja
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - F Jasmin Kappert
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
| | - Rui Ning Wang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Hugo Lourenço-Martins
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
| | - Zheru Qiu
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Junqiu Liu
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Ofer Kfir
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
| | - Tobias J Kippenberg
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.,Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Claus Ropers
- Max Planck Institute for Multidisciplinary Sciences, D-37077 Göttingen, Germany.,4th Physical Institute - Solids and Nanostructures, University of Göttingen, D-37077 Göttingen, Germany
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9
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Henke JW, Raja AS, Feist A, Huang G, Arend G, Yang Y, Kappert FJ, Wang RN, Möller M, Pan J, Liu J, Kfir O, Ropers C, Kippenberg TJ. Integrated photonics enables continuous-beam electron phase modulation. Nature 2021; 600:653-658. [PMID: 34937900 PMCID: PMC8695378 DOI: 10.1038/s41586-021-04197-5] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 11/01/2021] [Indexed: 11/10/2022]
Abstract
Integrated photonics facilitates extensive control over fundamental light-matter interactions in manifold quantum systems including atoms1, trapped ions2,3, quantum dots4 and defect centres5. Ultrafast electron microscopy has recently made free-electron beams the subject of laser-based quantum manipulation and characterization6-11, enabling the observation of free-electron quantum walks12-14, attosecond electron pulses10,15-17 and holographic electromagnetic imaging18. Chip-based photonics19,20 promises unique applications in nanoscale quantum control and sensing but remains to be realized in electron microscopy. Here we merge integrated photonics with electron microscopy, demonstrating coherent phase modulation of a continuous electron beam using a silicon nitride microresonator. The high-finesse (Q0 ≈ 106) cavity enhancement and a waveguide designed for phase matching lead to efficient electron-light scattering at extremely low, continuous-wave optical powers. Specifically, we fully deplete the initial electron state at a cavity-coupled power of only 5.35 microwatts and generate >500 electron energy sidebands for several milliwatts. Moreover, we probe unidirectional intracavity fields with microelectronvolt resolution in electron-energy-gain spectroscopy21. The fibre-coupled photonic structures feature single-optical-mode electron-light interaction with full control over the input and output light. This approach establishes a versatile and highly efficient framework for enhanced electron beam control in the context of laser phase plates22, beam modulators and continuous-wave attosecond pulse trains23, resonantly enhanced spectroscopy24-26 and dielectric laser acceleration19,20,27. Our work introduces a universal platform for exploring free-electron quantum optics28-31, with potential future developments in strong coupling, local quantum probing and electron-photon entanglement.
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Affiliation(s)
- Jan-Wilke Henke
- Georg-August-Universität Göttingen, Göttingen, Germany
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany
| | - Arslan Sajid Raja
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Armin Feist
- Georg-August-Universität Göttingen, Göttingen, Germany
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany
| | - Guanhao Huang
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Germaine Arend
- Georg-August-Universität Göttingen, Göttingen, Germany
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany
| | - Yujia Yang
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - F Jasmin Kappert
- Georg-August-Universität Göttingen, Göttingen, Germany
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany
| | - Rui Ning Wang
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Marcel Möller
- Georg-August-Universität Göttingen, Göttingen, Germany
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany
| | - Jiahe Pan
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Junqiu Liu
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Ofer Kfir
- Georg-August-Universität Göttingen, Göttingen, Germany
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany
| | - Claus Ropers
- Georg-August-Universität Göttingen, Göttingen, Germany.
- Max Planck Institute of Multidisciplinary Sciences, Göttingen, Germany.
| | - Tobias J Kippenberg
- Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland.
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10
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Karnieli A, Rivera N, Arie A, Kaminer I. Superradiance and Subradiance due to Quantum Interference of Entangled Free Electrons. PHYSICAL REVIEW LETTERS 2021; 127:060403. [PMID: 34420316 DOI: 10.1103/physrevlett.127.060403] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Accepted: 06/23/2021] [Indexed: 06/13/2023]
Abstract
When multiple quantum emitters radiate, their emission rate may be enhanced or suppressed due to collective interference in a process known as super- or subradiance. Such processes are well known to occur also in light emission from free electrons, known as coherent cathodoluminescence. Unlike atomic systems, free electrons have an unbounded energy spectrum, and, thus, all their emission mechanisms rely on electron recoil, in addition to the classical properties of the dielectric medium. To date, all experimental and theoretical studies of super- and subradiance from free electrons assumed only classical correlations between particles. However, dependence on quantum correlations, such as entanglement between free electrons, has not been studied. Recent advances in coherent shaping of free-electron wave functions motivate the investigation of such quantum regimes of super- and subradiance. In this Letter, we show how a pair of coincident path-entangled electrons can demonstrate either super- or subradiant light emission, depending on the two-particle wave function. By choosing different free-electron Bell states, the spectrum and emission pattern of the light can be reshaped, in a manner that cannot be accounted for by a classical mixed state. We show these results for light emission in any optical medium and discuss their generalization to many-body quantum states. Our findings suggest that light emission can be sensitive to the explicit quantum state of the emitting matter wave and possibly serve as a nondestructive measurement scheme for measuring the quantum state of many-body systems.
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Affiliation(s)
- Aviv Karnieli
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - Nicholas Rivera
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ady Arie
- School of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Ido Kaminer
- Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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11
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Di Giulio V, Kfir O, Ropers C, García de Abajo FJ. Modulation of Cathodoluminescence Emission by Interference with External Light. ACS NANO 2021; 15:7290-7304. [PMID: 33724007 PMCID: PMC8939848 DOI: 10.1021/acsnano.1c00549] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 02/18/2021] [Indexed: 05/20/2023]
Abstract
Spontaneous processes triggered in a sample by free electrons, such as cathodoluminescence, are commonly regarded and detected as stochastic events. Here, we supplement this picture by showing through first-principles theory that light and free-electron pulses can interfere when interacting with a nanostructure, giving rise to a modulation in the spectral distribution of the cathodoluminescence light emission that is strongly dependent on the electron wave function. Specifically, for a temporally focused electron, cathodoluminescence can be canceled upon illumination with a spectrally modulated dimmed laser that is phase-locked relative to the electron density profile. We illustrate this idea with realistic simulations under attainable conditions in currently available ultrafast electron microscopes. We further argue that the interference between excitations produced by light and free electrons enables the manipulation of the ultrafast materials response by combining the spectral and temporal selectivity of the light with the atomic resolution of electron beams.
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Affiliation(s)
- Valerio Di Giulio
- ICFO-Institut de
Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Ofer Kfir
- IV Physical Institute,
Solids and Nanostructures, University of
Göttingen, 37077 Göttingen, Germany
- Max Planck
Institute for Biophysical Chemistry (MPIBPC), 37077 Göttingen, Germany
| | - Claus Ropers
- IV Physical Institute,
Solids and Nanostructures, University of
Göttingen, 37077 Göttingen, Germany
- Max Planck
Institute for Biophysical Chemistry (MPIBPC), 37077 Göttingen, Germany
| | - F. Javier García de Abajo
- ICFO-Institut de
Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis
Avançats, Passeig
Lluís Companys 23, 08010 Barcelona, Spain
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12
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García
de Abajo FJ, Di Giulio V. Optical Excitations with Electron Beams: Challenges and Opportunities. ACS PHOTONICS 2021; 8:945-974. [PMID: 35356759 PMCID: PMC8939335 DOI: 10.1021/acsphotonics.0c01950] [Citation(s) in RCA: 42] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 02/17/2021] [Accepted: 02/19/2021] [Indexed: 05/20/2023]
Abstract
Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.
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Affiliation(s)
- F. Javier García
de Abajo
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA-Institució
Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
- E-mail:
| | - Valerio Di Giulio
- ICFO-Institut
de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, 08860 Castelldefels, Barcelona, Spain
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13
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Kfir O, Di Giulio V, de Abajo FJG, Ropers C. Optical coherence transfer mediated by free electrons. SCIENCE ADVANCES 2021; 7:eabf6380. [PMID: 33931451 PMCID: PMC8087403 DOI: 10.1126/sciadv.abf6380] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 02/16/2021] [Indexed: 05/03/2023]
Abstract
We theoretically investigate the quantum-coherence properties of the cathodoluminescence (CL) emission produced by a temporally modulated electron beam. Specifically, we consider the quantum-optical correlations of CL produced by electrons that are previously shaped by a laser field. Our main prediction is the presence of phase correlations between the emitted CL field and the electron-modulating laser, even though the emission intensity and spectral profile are independent of the electron state. In addition, the coherence of the CL field extends to harmonics of the laser frequency. Since electron beams can be focused to below 1 Å, their ability to transfer optical coherence could enable the ultra-precise excitation, manipulation, and spectrally resolved probing of nanoscale quantum systems.
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Affiliation(s)
- Ofer Kfir
- University of Göttingen, IV. Physical Institute, Göttingen, Germany.
- Max Planck Institute for Biophysical Chemistry (MPIBPC), Göttingen, Germany
| | - Valerio Di Giulio
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - F Javier García de Abajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
| | - Claus Ropers
- University of Göttingen, IV. Physical Institute, Göttingen, Germany
- Max Planck Institute for Biophysical Chemistry (MPIBPC), Göttingen, Germany
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14
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Cohen M, Salomon A. Secondary Electron Cloaking with Broadband Plasmonic Resonant Absorbers. J Phys Chem Lett 2017; 8:3912-3916. [PMID: 28745891 DOI: 10.1021/acs.jpclett.7b00869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Scanning electron microscopy (SEM) is one of the most powerful tools for nanoscale inspection and imaging. It is broadly used for biomedicine, materials science, and nanotechnology, enabling spatial resolution beyond the optical diffraction limit. In SEM, a high-energy electron beam illuminates a specimen, and the emitted secondary electrons are routed to a positively biased, synchronized detector for image creation. Here, for the first time, we experimentally demonstrate a cloaking of metallic objects from a secondary electron image. We make a metallic disc with a diameter of 300 nm almost invisible to a secondary electron detector with <5 nm spatial resolution. The secondary electron cloaking is based on broadband optical radiation absorption in the near field. Our secondary electron images are in good agreement with full-wave numerical solution of Maxwell's equations at optical frequencies, confirming the concept of secondary electron cloaking based on broadband optical radiation absorption.
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Affiliation(s)
- Moshik Cohen
- Faculty of Engineering, Bar-Ilan University , Ramat-Gan 52900, Israel
- Bar-Ilan Institute for Nanotechnology & Advanced Materials , Ramat-Gan 52900, Israel
| | - Adi Salomon
- Department of Chemistry, Bar-Ilan University , Ramat-Gan 52900, Israel
- Bar-Ilan Institute for Nanotechnology & Advanced Materials , Ramat-Gan 52900, Israel
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15
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Cohen M, Abulafia Y, Shavit R, Zalevsky Z. Secondary Electron Imaging of Light at the Nanoscale. ACS NANO 2017; 11:3274-3281. [PMID: 28264151 DOI: 10.1021/acsnano.7b00548] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The interaction of fast electrons with metal atoms may lead to optical excitations. This exciting phenomenon forms the basis for the most powerful inspection methods in nanotechnology, such as cathodoluminescence and electron-energy loss spectroscopy. However, direct nanoimaging of light based on electrons is yet to be introduced. Here, we experimentally demonstrate simultaneous excitation and nanoimaging of optical signals using unmodified scanning electron microscope. We use high-energy electron beam for plasmon excitation and rapidly image the optical near fields using the emitted secondary electrons. We analyze dipole nanoantennas coupled with channel nanoplasmonic waveguides and observe both surface plasmons and surface plasmon polaritons with spatial resolution of 25 nm. Our experimental results are confirmed by rigorous numerical calculations based on full-wave solution of Maxwell's equations, showing high correlation between optical near fields and secondary electrons images. This demonstration of optical near-field mapping using direct electron imaging provides essential insights to the exciting relations between electrons plasmons and photons, paving the way toward secondary electron-based plasmon analysis at the nanoscale.
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Affiliation(s)
- Moshik Cohen
- Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev , Beer-Sheva 84105, Israel
| | | | - Reuven Shavit
- Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev , Beer-Sheva 84105, Israel
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16
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Cherqui C, Thakkar N, Li G, Camden JP, Masiello DJ. Characterizing Localized Surface Plasmons Using Electron Energy-Loss Spectroscopy. Annu Rev Phys Chem 2016; 67:331-57. [DOI: 10.1146/annurev-physchem-040214-121612] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Charles Cherqui
- Department of Chemistry, University of Washington, Seattle, Washington 98195;
| | - Niket Thakkar
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195
| | - Guoliang Li
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556;
| | - Jon P. Camden
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556;
| | - David J. Masiello
- Department of Chemistry, University of Washington, Seattle, Washington 98195;
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195
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17
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Vardi Y, Cohen-Hoshen E, Shalem G, Bar-Joseph I. Fano Resonance in an Electrically Driven Plasmonic Device. NANO LETTERS 2016; 16:748-752. [PMID: 26717292 DOI: 10.1021/acs.nanolett.5b04622] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present an electrically driven plasmonic device consisting of a gold nanoparticle trapped in a gap between two electrodes. The tunneling current in the device generates plasmons, which decay radiatively. The emitted spectrum extends up to an energy that depends on the applied voltage. Characterization of the electrical conductance at low temperatures allows us to extract the voltage drop on each tunnel barrier and the corresponding emitted spectrum. In several devices we find a pronounced sharp asymmetrical dip in the spectrum, which we identify as a Fano resonance. Finite-difference time-domain calculations reveal that this resonance is due to interference between the nanoparticle and electrodes dipolar fields and can be conveniently controlled by the structural parameters.
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Affiliation(s)
- Yuval Vardi
- Department of Condensed Matter Physics, Weizmann Institute of Science , Rehovot 76100, Israel
| | - Eyal Cohen-Hoshen
- Department of Condensed Matter Physics, Weizmann Institute of Science , Rehovot 76100, Israel
| | - Guy Shalem
- Department of Condensed Matter Physics, Weizmann Institute of Science , Rehovot 76100, Israel
| | - Israel Bar-Joseph
- Department of Condensed Matter Physics, Weizmann Institute of Science , Rehovot 76100, Israel
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18
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Raggi G, Stace AJ, Bichoutskaia E. Polarisation charge switching through the motion of metal atoms trapped in fullerene cages. Phys Chem Chem Phys 2014; 16:23869-73. [PMID: 25272966 DOI: 10.1039/c4cp02672a] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The formation of an endohedral fullerene can lead to charge transfer and the generation of a trapped positively charged metal ion. Using Ca@C60 and [Ca@C60](+) endohedral fullerenes as models, density functional theory calculations predict that the motion of a calcium ion within a fullerene is accompanied by large changes in electron density on the surrounding carbon cage. In the case of [Ca@C60](+), partial atomic charge distribution on the carbon cage is split between hemispheres into regions of positive and negative charge as Ca(n+) moves inside the fullerene cage (non-integer n strongly depends on position of the ion). It is proposed that within tethered fullerene cages the movement of partial atomic charge could form the bases of a molecular polarisation storage bit, and that adopted in the form of [Ca@C60](+) the presence of an overall charge may offer a route to either optical or electronic control.
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Affiliation(s)
- G Raggi
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
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19
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Tizei LHG, Kociak M. Spatially resolved quantum nano-optics of single photons using an electron microscope. PHYSICAL REVIEW LETTERS 2013; 110:153604. [PMID: 25167267 DOI: 10.1103/physrevlett.110.153604] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2013] [Revised: 02/15/2013] [Indexed: 05/25/2023]
Abstract
We report on the experimental demonstration of single-photon state generation and characterization in an electron microscope. In this aim we have used low intensity relativistic (energy between 60 and 100 keV) electrons beams focused in a ca. 1 nm probe to excite diamond nanoparticles. This triggered individual neutral nitrogen-vacancy centers to emit photons which could be gathered and sent to a Hanbury Brown-Twiss intensity interferometer. The detection of a dip in the correlation function at small time delays clearly demonstrates antibunching and thus the creation of nonclassical light states. Specifically, we have also demonstrated single-photon states detection. We unveil the mechanism behind quantum states generation in an electron microscope, and show that it clearly makes cathodoluminescence the nanometer scale analog of photoluminescence. By using an extremely small electron probe size and the ability to monitor its position with subnanometer resolution, we also show the possibility of measuring the quantum character of the emitted beam with deep subwavelength resolution.
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Affiliation(s)
- L H G Tizei
- Laboratoire de Physique des Solides, Université Paris-Sud, CNRS-UMR 8502, Orsay 91405, France
| | - M Kociak
- Laboratoire de Physique des Solides, Université Paris-Sud, CNRS-UMR 8502, Orsay 91405, France
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