Resonant scattering of a single atom with gain: A wave-function-diagrammatic approach

Wave function collapse has been a contentious concept in quantum mechanics for a considerable time. Here we show examples of how the concept can be used to advantage in predicting the statistical results of three experiments in atomic physics and quantum optics: photon antibunching, single-photon phase difference states and interrupted single-atom fluorescence. We examine the question of whether or not collapse is 'really' a physical process, and discuss the consequences of simply omitting it but including the observer as a part of the overall system governed by the laws of quantum mechanics. The resulting entangled world does not appear to be inconsistent with experience.

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Computer simulation of phase of contrast of cluster atoms on support film made by sputter deposition

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108313 ◽

1978 ◽

Vol 36 (1) ◽

pp. 234-235

Author(s):

Tetsuo Oikawa ◽

Fumiko Ishigaki ◽

Shuhei Fukuyama ◽

Haruo Wakizaka ◽

Kiichi Hojou ◽

...

Keyword(s):

Wave Function ◽

Scattering Amplitude ◽

Spherical Aberration ◽

Gold Cluster ◽

Sputter Deposition ◽

Single Atom ◽

Diffraction Integral ◽

The Monte Carlo Method ◽

Kirchhoff Diffraction Integral ◽

Image Position

Based on the image formation theory, the wave function of a single atom consisting of the complex scattering amplitude |f(0)|exp{-inj(0)} and phase shift γj of spherical aberration is rigorously obtained by the Kirchhoff diffraction integral in the Fraunhofer approximation as a function of defocus. Using of the wave function w(υj,γj) of a group of atoms, which is extended the wave function of a single atom, variations of imaging phase contrast of tungsten support film in through focal series made by sputter deposition are simulated. The contrast of tungsten support film and a gold cluster atoms on the substrate made by sputter depposition, which are very close with the experiment, are calculated by the Monte-Carlo method with the aid of the inter-atomic size distribution measured by electron diffraction pattern.The contrast g for cluster atoms has been calculated by integrating the scattering wave for coherent waves, and for incoherent waves the amplitude scattered outside the limiting angle α set by the aperture respectively,

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Wave function of a photon produced in the resonant scattering of twisted light by relativistic ions

Physical Review A ◽

10.1103/physreva.104.023101 ◽

2021 ◽

Vol 104 (2) ◽

Author(s):

Dmitry V. Karlovets ◽

Valeriy G. Serbo ◽

Andrey Surzhykov

Keyword(s):

Wave Function ◽

Resonant Scattering ◽

Twisted Light

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Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051840 ◽

1974 ◽

Vol 32 ◽

pp. 366-367

Author(s):

Wah Chi

Keyword(s):

Scattering Amplitude ◽

Present Report ◽

Dark Field ◽

Image Contrast ◽

Single Atom ◽

Optical Theorem ◽

Hartree Fock ◽

Heavy Atoms ◽

Beam Stop ◽

Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

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Analytic integration of contrast transfer functions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010010617x ◽

1988 ◽

Vol 46 ◽

pp. 822-823

Author(s):

Peter Rez

Keyword(s):

Wave Function ◽

Transfer Function ◽

Transfer Functions ◽

Spherical Aberration ◽

Continuous Distribution ◽

Objective Lens ◽

Direction Parallel ◽

Scattering Angle ◽

Analytic Integration ◽

Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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Atomic Spectroscopy in the FIM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100145157 ◽

1986 ◽

Vol 44 ◽

pp. 758-761

Author(s):

J. J. Hren ◽

S. D. Walck

Keyword(s):

Electron Microscope ◽

Electric Fields ◽

Atom Probe ◽

Atomic Spectroscopy ◽

Single Atom ◽

Statistical Sampling ◽

Commercial Instrument ◽

Available Technology ◽

High Electric Fields ◽

Field Ion Microscope

The field ion microscope (FIM) has had the ability to routinely image the surface atoms of metals since Mueller perfected it in 1956. Since 1967, the TOF Atom Probe has had single atom sensitivity in conjunction with the FIM. “Why then hasn't the FIM enjoyed the success of the electron microscope?” The answer is closely related to the evolution of FIM/Atom Probe techniques and the available technology. This paper will review this evolution from Mueller's early discoveries, to the development of a viable commercial instrument. It will touch upon some important contributions of individuals and groups, but will not attempt to be all inclusive. Variations in instrumentation that define the class of problems for which the FIM/AP is uniquely suited and those for which it is not will be described. The influence of high electric fields inherent to the technique on the specimens studied will also be discussed. The specimen geometry as it relates to preparation, statistical sampling and compatibility with the TEM will be examined.

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Field ion microscope investigations of atomic processes at surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100153117 ◽

1989 ◽

Vol 47 ◽

pp. 228-229

Author(s):

G. L. Kellogg ◽

P. R. Schwoebel

Keyword(s):

Single Crystal ◽

Crystal Surface ◽

Linear Chain ◽

Atom Probe ◽

Nucleation And Growth ◽

Single Atom ◽

Initial Structure ◽

Atomic Processes ◽

Single Crystal Surfaces ◽

Field Ion Microscope

Although no longer unique in its ability to resolve individual single atoms on surfaces, the field ion microscope remains a powerful tool for the quantitative characterization of atomic processes on single-crystal surfaces. Investigations of single-atom surface diffusion, adatom-adatom interactions, surface reconstructions, cluster nucleation and growth, and a variety of surface chemical reactions have provided new insights to the atomic nature of surfaces. Moreover, the ability to determine the chemical identity of selected atoms seen in the field ion microscope image by atom-probe mass spectroscopy has increased or even changed our understanding of solid-state-reaction processes such as ordering, clustering, precipitation and segregation in alloys. This presentation focuses on the operational principles of the field-ion microscope and atom-probe mass spectrometer and some very recent applications of the field ion microscope to the nucleation and growth of metal clusters on metal surfaces.The structure assumed by clusters of atoms on a single-crystal surface yields fundamental information on the adatom-adatom interactions important in crystal growth. It was discovered in previous investigations with the field ion microscope that, contrary to intuition, the initial structure of clusters of Pt, Pd, Ir and Ni atoms on W(110) is a linear chain oriented in the <111> direction of the substrate.

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Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179129 ◽

1990 ◽

Vol 48 (1) ◽

pp. 74-75

Author(s):

D.E. Jesson ◽

S. J. Pennycook

Keyword(s):

Wave Function ◽

Electron Scattering ◽

Numerical Solutions ◽

Large Angle ◽

Real Space ◽

High Angle ◽

Analytical Treatment ◽

Order Zero ◽

Experimental Conditions ◽

Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

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Recent advancement in the electrocatalytic synthesis of ammonia

Nanoscale ◽

10.1039/d0nr01359e ◽

2020 ◽

Vol 12 (15) ◽

pp. 8065-8094 ◽

Cited By ~ 6

Author(s):

Xudong Wen ◽

Jingqi Guan

Keyword(s):

Metal Oxide ◽

Oxide Catalysts ◽

Single Atom ◽

Metal Oxide Catalysts ◽

Metal Free ◽

Recent Advancement ◽

Nanocomposite Catalysts

Different kinds of electrocatalysts used in NRR electrocatalysis (including single atom catalysts, metal oxide catalysts, nanocomposite catalysts, and metal free catalysts) are introduced.

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