Optical Excitations with Electron Beams: Challenges and Opportunities.
TL;DR: In this paper, it was shown 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.
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-Angstrom--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 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 perspectives on various exciting directions for disruptive approaches to non-invasive 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 applications in optical modulation of electron beams.
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TL;DR: In this paper, the authors show that for fixed optical intensity, phase-squeezed light can be used to accelerate the compression of free electron pulses, while amplitude squeezing produces ultrashort double-pulse profiles.
Abstract: Controlling the wave function of free electrons is important to improve the spatial resolution of electron microscopes, the efficiency of electron interaction with sample modes of interest, and our ability to probe ultrafast materials dynamics at the nanoscale. In this context, attosecond electron compression has been recently demonstrated through interaction with the near fields created by scattering of ultrashort laser pulses at nanostructures followed by free electron propagation. Here, we show that control over electron pulse shaping, compression, and statistics can be improved by replacing coherent laser excitation by interaction with quantum light. We find that compression is accelerated for fixed optical intensity by using phase-squeezed light, while amplitude squeezing produces ultrashort double-pulse profiles. The generated electron pulses exhibit periodic revivals in complete analogy to the optical Talbot effect. We further reveal that the coherences created in a sample by interaction with the modulated electron are strongly dependent on the statistics of the modulating light, while the diagonal part of the sample density matrix reduces to a Poissonian distribution regardless of the type of light used to shape the electron. The present study opens a new direction toward the generation of free electron pulses with additional control over duration, shape, and statistics, which directly affect their interaction with a sample.
13 citations
References
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TL;DR: In this paper, a theoretical analysis of the shape of the 2s2p^{1}P resonance of He observed in the inelastic scattering of electrons is presented. But the analysis is restricted to the case of one discrete level with two or more continua and of a set of discrete levels with one continuum.
Abstract: The interference of a discrete autoionized state with a continuum gives rise to characteristically asymmetric peaks in excitation spectra. The earlier qualitative interpretation of this phenomenon is extended and revised. A theoretical formula is fitted to the shape of the $2s2p^{1}P$ resonance of He observed in the inelastic scattering of electrons. The fitting determines the parameters of the $2s2p^{1}P$ resonance as follows: $E=60.1$ ev, $\ensuremath{\Gamma}\ensuremath{\sim}0.04$ ev, $f\ensuremath{\sim}2 \mathrm{to} 4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The theory is extended to the interaction of one discrete level with two or more continua and of a set of discrete levels with one continuum. The theory can also give the position and intensity shifts produced in a Rydberg series of discrete levels by interaction with a level of another configuration. The connection with the nuclear theory of resonance scattering is indicated.
8,210 citations
TL;DR: This work introduced a method for optically imaging intracellular proteins at nanometer spatial resolution and used this method to image specific target proteins in thin sections of lysosomes and mitochondria and in fixed whole cells to image retroviral protein Gag at the plasma membrane.
Abstract: We introduce a method for optically imaging intracellular proteins at nanometer spatial resolution. Numerous sparse subsets of photoactivatable fluorescent protein molecules were activated, localized (to approximately 2 to 25 nanometers), and then bleached. The aggregate position information from all subsets was then assembled into a superresolution image. We used this method--termed photoactivated localization microscopy--to image specific target proteins in thin sections of lysosomes and mitochondria; in fixed whole cells, we imaged vinculin at focal adhesions, actin within a lamellipodium, and the distribution of the retroviral protein Gag at the plasma membrane.
7,924 citations
TL;DR: The interest in nanoscale materials stems from the fact that new properties are acquired at this length scale and, equally important, that these properties are equally important.
Abstract: The interest in nanoscale materials stems from the fact that new properties are acquired at this length scale and, equally important, that these properties * To whom correspondence should be addressed. Phone, 404-8940292; fax, 404-894-0294; e-mail, mostafa.el-sayed@ chemistry.gatech.edu. † Case Western Reserve UniversitysMillis 2258. ‡ Phone, 216-368-5918; fax, 216-368-3006; e-mail, burda@case.edu. § Georgia Institute of Technology. 1025 Chem. Rev. 2005, 105, 1025−1102
6,852 citations
Book•
31 Dec 1995
TL;DR: In this article, the authors present an overview of the basic principles of energy-loss spectroscopy, including the use of the Wien filter, and the analysis of the inner-shell of the detector.
Abstract: 1. An Introduction to Electron Energy-Loss Spectroscopy.- 1.1 Interaction of Fast Electrons with a Solid.- 1.2. The Electron Energy-Loss Spectrum.- 1.3. The Development of Experimental Techniques.- 1.4. Comparison of Analytical Methods.- 1.4.1. Ion-Beam Methods.- 1.4.2. Incident Photons.- 1.4.3. Electron-Beam Techniques.- 1.5. Further Reading.- 2. Instrumentation for Energy-Loss Spectroscopy.- 2.1. Energy-Analyzing and Energy-Selecting Systems.- 2.1.1. The Magnetic-Prism Spectrometer.- 2.1.2. Energy-Selecting Magnetic-Prism Devices.- 2.1.3. The Wien Filter.- 2.1.4. Cylindrical-Lens Analyzers.- 2.1.5. Retarding-Field Analyzers.- 2.1.6. Electron Monochromators.- 2.2. The Magnetic-Prism Spectrometer.- 2.2.1. First-Order Properties.- 2.2.2. Higher-Order Focusing.- 2.2.3. Design of an Aberration-Corrected Spectrometer.- 2.2.4. Practical Considerations.- 2.2.5. Alignment and Adjustment of the Spectrometer.- 2.3. The Use of Prespectrometer Lenses.- 2.3.1. Basic Principles.- 2.3.2. CTEM with Projector Lens On.- 2.3.3. CTEM with Projector Lens Off.- 2.3.4. Spectrometer-Specimen Coupling in a High-Resolution STEM.- 2.4. Recording the Energy-Loss Spectrum.- 2.4.1. Serial Acquisition.- 2.4.2. Electron Detectors for Serial Recording.- 2.4.3. Scanning the Energy-Loss Spectrum.- 2.4.4. Signal Processing and Storage.- 2.4.5. Noise Performance of a Serial Detector.- 2.4.6. Parallel-Recording Detectors.- 2.4.7. Direct Exposure of a Diode-Array Detector.- 2.4.8. Indirect Exposure of a Diode Array.- 2.4.9. Removal of Diode-Array Artifacts.- 2.5. Energy-Filtered Imaging.- 2.5.1. Elemental Mapping.- 2.5.2. Z-Contrast Imaging.- 3. Electron Scattering Theory.- 3.1. Elastic Scattering.- 3.1.1. General Formulas.- 3.1.2. Atomic Models.- 3.1.3. Diffraction Effects.- 3.1.4. Electron Channeling.- 3.1.5. Phonon Scattering.- 3.2. Inelastic Scattering.- 3.2.1. Atomic Models.- 3.2.2. Bethe Theory.- 3.2.3. Dielectric Formulation.- 3.2.4. Solid-State Effects.- 3.3. Excitation of Outer-Shell Electrons.- 3.3.1. Volume Plasmons.- 3.3.2. Single-Electron Excitation.- 3.3.3. Excitons.- 3.3.4. Radiation Losses.- 3.3.5. Surface Plasmons.- 3.3.6. Single, Plural, and Multiple Scattering.- 3.4. Inner-Shell Excitation.- 3.4.1. Generalized Oscillator Strength.- 3.4.2. Kinematics of Scattering.- 3.4.3. Ionization Cross Sections.- 3.5. The Spectral Background to Inner-Shell Edges.- 3.6. The Structure of Inner-Shell Edges.- 3.6.1. Basic Edge Shapes.- 3.6.2. Chemical Shifts in Threshold Energy.- 3.6.3. Near-Edge Fine Structure (ELNES).- 3.6.4. Extended Energy-Loss Fine Structure (EXELFS).- 4. Quantitative Analysis of the Energy-Loss Spectrum.- 4.1. Removal of Plural Scattering from the Low-Loss Region.- 4.1.1. Fourier-Log Deconvolution.- 4.1.2. Approximate Methods.- 4.1.3. Angular-Dependent Deconvolution.- 4.2. Kramers-Kronig Analysis.- 4.3. Removal of Plural Scattering from Inner-Shell Edges.- 4.3.1. Fourier-Log Deconvolution.- 4.3.2. Fourier-Ratio Method.- 4.3.3. Van Cittert'1. An Introduction to Electron Energy-Loss Spectroscopy.- 1.1 Interaction of Fast Electrons with a Solid.- 1.2. The Electron Energy-Loss Spectrum.- 1.3. The Development of Experimental Techniques.- 1.4. Comparison of Analytical Methods.- 1.4.1. Ion-Beam Methods.- 1.4.2. Incident Photons.- 1.4.3. Electron-Beam Techniques.- 1.5. Further Reading.- 2. Instrumentation for Energy-Loss Spectroscopy.- 2.1. Energy-Analyzing and Energy-Selecting Systems.- 2.1.1. The Magnetic-Prism Spectrometer.- 2.1.2. Energy-Selecting Magnetic-Prism Devices.- 2.1.3. The Wien Filter.- 2.1.4. Cylindrical-Lens Analyzers.- 2.1.5. Retarding-Field Analyzers.- 2.1.6. Electron Monochromators.- 2.2. The Magnetic-Prism Spectrometer.- 2.2.1. First-Order Properties.- 2.2.2. Higher-Order Focusing.- 2.2.3. Design of an Aberration-Corrected Spectrometer.- 2.2.4. Practical Considerations.- 2.2.5. Alignment and Adjustment of the Spectrometer.- 2.3. The Use of Prespectrometer Lenses.- 2.3.1. Basic Principles.- 2.3.2. CTEM with Projector Lens On.- 2.3.3. CTEM with Projector Lens Off.- 2.3.4. Spectrometer-Specimen Coupling in a High-Resolution STEM.- 2.4. Recording the Energy-Loss Spectrum.- 2.4.1. Serial Acquisition.- 2.4.2. Electron Detectors for Serial Recording.- 2.4.3. Scanning the Energy-Loss Spectrum.- 2.4.4. Signal Processing and Storage.- 2.4.5. Noise Performance of a Serial Detector.- 2.4.6. Parallel-Recording Detectors.- 2.4.7. Direct Exposure of a Diode-Array Detector.- 2.4.8. Indirect Exposure of a Diode Array.- 2.4.9. Removal of Diode-Array Artifacts.- 2.5. Energy-Filtered Imaging.- 2.5.1. Elemental Mapping.- 2.5.2. Z-Contrast Imaging.- 3. Electron Scattering Theory.- 3.1. Elastic Scattering.- 3.1.1. General Formulas.- 3.1.2. Atomic Models.- 3.1.3. Diffraction Effects.- 3.1.4. Electron Channeling.- 3.1.5. Phonon Scattering.- 3.2. Inelastic Scattering.- 3.2.1. Atomic Models.- 3.2.2. Bethe Theory.- 3.2.3. Dielectric Formulation.- 3.2.4. Solid-State Effects.- 3.3. Excitation of Outer-Shell Electrons.- 3.3.1. Volume Plasmons.- 3.3.2. Single-Electron Excitation.- 3.3.3. Excitons.- 3.3.4. Radiation Losses.- 3.3.5. Surface Plasmons.- 3.3.6. Single, Plural, and Multiple Scattering.- 3.4. Inner-Shell Excitation.- 3.4.1. Generalized Oscillator Strength.- 3.4.2. Kinematics of Scattering.- 3.4.3. Ionization Cross Sections.- 3.5. The Spectral Background to Inner-Shell Edges.- 3.6. The Structure of Inner-Shell Edges.- 3.6.1. Basic Edge Shapes.- 3.6.2. Chemical Shifts in Threshold Energy.- 3.6.3. Near-Edge Fine Structure (ELNES).- 3.6.4. Extended Energy-Loss Fine Structure (EXELFS).- 4. Quantitative Analysis of the Energy-Loss Spectrum.- 4.1. Removal of Plural Scattering from the Low-Loss Region.- 4.1.1. Fourier-Log Deconvolution.- 4.1.2. Approximate Methods.- 4.1.3. Angular-Dependent Deconvolution.- 4.2. Kramers-Kronig Analysis.- 4.3. Removal of Plural Scattering from Inner-Shell Edges.- 4.3.1. Fourier-Log Deconvolution.- 4.3.2. Fourier-Ratio Method.- 4.3.3. Van Cittert's Method.- 4.3.4. Effect of a Collection Aperture.- 4.4. Background Fitting to Ionization Edges.- 4.4.1. Energy Dependence of the Background.- 4.4.2. Background-Fitting Procedures.- 4.4.3. Background-Subtraction Errors.- 4.5. Elemental Analysis Using Inner-Shell Edges.- 4.5.1. Basic Formulas.- 4.5.2. Correction for Incident-Beam Convergence.- 4.5.3. Effect of Sample Orientation.- 4.5.4. Effect of Specimen Thickness.- 4.5.5. Choice of Collection Angle.- 4.5.6. Choice of Integration and Fitting Regions.- 4.5.7. Microanalysis Software.- 4.5.8. Calculation of Partial Cross Sections.- 4.6. Analysis of Extended Energy-Loss Fine Structure.- 4.6.1. Spectrum Acquisition.- 4.6.2. Fourier-Transform Method of Data Analysis.- 4.6.3. Curve-Fitting Procedure.- 5. Applications of Energy-Loss Spectroscopy.- 5.1. Measurement of Specimen Thickness.- 5.1.1. Measurement of Absolute Thickness.- 5.1.2. Sum-Rule Methods.- 5.2. Low-Loss Spectroscopy.- 5.2.1. Phase Identification.- 5.2.2. Measurement of Alloy Composition.- 5.2.3. Detection of Hydrogen and Helium.- 5.2.4. Zero-Loss Images.- 5.2.5. Z-contrast Images.- 5.2.6. Plasmon-Loss Images.- 5.3. Core-Loss Microanalysis.- 5.3.1. Choice of Specimen Thickness and Incident Energy.- 5.3.2. Specimen Preparation.- 5.3.3. Elemental Detection and Mapping.- 5.3.4. Quantitative Microanalysis.- 5.3.5. Measurement and Control of Radiation Damage.- 5.4. Spatial Resolution and Elemental Detection Limits.- 5.4.1. Electron-Optical Considerations.- 5.4.2. Loss of Resolution due to Electron Scattering.- 5.4.3. Statistical Limitations.- 5.4.4. Localization of Inelastic Scattering.- 5.5. Structural Information from EELS.- 5.5.1. Low-Loss Fine Structure.- 5.5.2. Orientation Dependence of Core-Loss Edges.- 5.5.3. Core-Loss Diffraction Patterns.- 5.5.4. Near-Edge Fine Structure.- 5.5.5. Extended Fine Structure.- 5.5.6. Electron-Compton Measurements.- Appendix A. Relativistic Bethe Theory.- Appendix B. FORTRAN Programs.- B.3. Incident-Convergence Correction.- B.4. Fourier-Log Deconvolution.- B.5. Kramers-Kronig Transformation.- Appendix C. Plasmon Energies of Some Elements and Compounds.- Appendix D. Inner-Shell Binding Energies and Edge Shapes.- Appendix E. Electron Wavelengths and Relativistic Factors Fundamental Constants.- References.
3,732 citations
TL;DR: Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches as discussed by the authors, where the central limit theorem implies that the reduction is proportional to the square root of the number of repetitions.
Abstract: The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections.
2,977 citations