Atomic scale electron vortices for nanoresearch

Verbeeck, Johan; Schattschneider, P.; Lazar, Sorin; Stöger-Pollach, Michael; Löffler, Stefan; Steiger‐Thirsfeld, Andreas; Tendeloo, Gustaaf Van

doi:10.1063/1.3662012

Cited by 104 publications

(97 citation statements)

References 31 publications

(36 reference statements)

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“…The case with σσ b ∼ 1 is realized, for instance, for 300-keV electrons focused in a spot of 1Å [21]; and now Σ 2 ≈ 1/(2σ 2 b ).…”

Section: Jhep03(2017)049mentioning

confidence: 95%

“…They were shown to be solutions of the wave equations [7][8][9][10][11][12][13][14], and the corresponding beams of photons, electrons, and neutrons were generated in recent years [15][16][17][18][19][20]. Vortex electrons with the kinetic energy of 200 − 300 keV can be focused to a spot of anÅngström size [21], their OAM can be as high as = 200 [22], their magnetic moment increases proportionally to [13], and this brings about new effects in the electromagnetic radiation [23,24]. Such photons and electrons were also proved useful for optical manipulation [14], for probing phase of a transition amplitude, for creating pairs entangled in their OAM [25][26][27][28][29][30], etc.…”

Section: Non-plane-wave Statesmentioning

confidence: 99%

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Scattering of wave packets with phases

Karlovets

2017

J. High Energ. Phys.

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A general problem of 2 → N f scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in (3 + 1) D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet σ p / p as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum t are discussed.

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“…The case with σσ b ∼ 1 is realized, for instance, for 300-keV electrons focused in a spot of 1Å [21]; and now Σ 2 ≈ 1/(2σ 2 b ).…”

Section: Jhep03(2017)049mentioning

confidence: 95%

Section: Non-plane-wave Statesmentioning

confidence: 99%

Scattering of wave packets with phases

Karlovets

2017

J. High Energ. Phys.

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“…This effect is of similar order of magnitude as that obtained with low OAM vortex beams and thus deemed possible but challenging to detect experimentally. Considering continuous technological improvements related to electron vortex beams [6][7][8]14,27,42,43 , spin polarization technology 15 and aberration correctors 41,44 , the present work will hopefully stimulate various experimental efforts to detect magnetism based on the suggested effects. An analysis of errors due to, e.g., sample drift and tilt suggests again that it will be very challenging to perform atomic resolution measurements while nanometer resolution measurements are expected to be more feasible.…”

Section: Discussionmentioning

confidence: 99%

Magnetic effects in the paraxial regime of elastic electron scattering

2016

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Based on a recent claim [Phys. Rev. Lett. 116, 127203 (2016)] that electron vortex can be used to image magnetism at the nanoscale in elastic scattering experiments, using transmission electron microscopy, a comprehensive computational study is performed to study magnetic effects in the paraxial regime of elastic electron scattering in magnetic solids. Magnetic interactions from electron vortex beams, spin polarized electron beams and beams with phase aberrations are considered, as they pass through ferromagnetic FePt or antiferromagnetic LaMnAsO. The magnetic signals are obtained by comparing the intensity over a disk in the diffraction plane for beams with opposite angular momentum or aberrations. The strongest magnetic signals are obtained from vortex beams with large orbital angular momentum, where relative magnetic signals above 10 −3 are indicated for 10 orbital angular momentum, meaning that relative signals of one percent could be expected with the even larger orbital angular momenta, which have been produced in experimental setups. All results indicate that beams with low acceleration voltage and small convergence angles yield stronger magnetic signals, which is unfortunately problematic for the possibility of high spatial resolution imaging. Nevertheless, under atomic resolution conditions, relative magnetic signals in the order of 10 −4 are demonstrated, corresponding to an increase with one order of magnitude compared to previous work.

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“…For a hydrogen atom, a is just a Bohr radius, a ≈ 0.053 nm. As beams of the electrons with σ x ∼ 0.1 nm have been already obtained [17,18], one can probe the highly nonclassical regime of scattering, in which negative values of the Wigner functions give noticeable contribution to the cross section. The simplest effect here would also be an azimuthal asymmetry in elastic scattering of a Schrödinger cat state off an atom, which would be of the order of a/σ x ∼ 10 −1 (see details in [6]).…”

Section: Going Beyond the Wkb Regimementioning

confidence: 99%

“…The asymmetry can reveal itself, say, in ee, e + e − , pp, or pp collisions (see also [15,16]), and it can be measured, for instance, by taking two electron beams, each focused to a spot of 0.1 nm, as in the Refs. [17,18], and colliding them slightly off-center at an impact parameter of b ∼ σ x . The order of the predicted asymmetry, very roughly, is…”

Section: Corrections To the Plane-wave Cross Sectionmentioning

confidence: 99%

Quantum scattering beyond the plane-wave approximation

Karlovets

2017

J. Phys.: Conf. Ser.

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Abstract. While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.

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Atomic scale electron vortices for nanoresearch

Cited by 104 publications

References 31 publications

Scattering of wave packets with phases

Scattering of wave packets with phases

Magnetic effects in the paraxial regime of elastic electron scattering

Quantum scattering beyond the plane-wave approximation

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