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arXiv:1710.09291 · Journal of Physics Conference Series

Quantum scattering beyond the plane-wave approximation

Dmitry V. Karlovets

Published Dec 1, 2017• 5 citations
arXivHTMLPDF

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.

DOI
10.1088/1742-6596/938/1/012031

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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.
Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays positive everywhere, which obscures such purely quantum phenomena as nonlocality and entanglement. With the advent of the electron microscopes with subnanometer-sized beams, one can enter a genuinely quantum regime where the latter effects become only moderately attenuated. Here we show how to probe negative values of the Wigner function in scattering of a coherent superposition of two Gaussian packets with a nonvanishing impact parameter between them (a Schrödinger's cat state) by atomic targets. For hydrogen in the ground 1s state, a small parameter of the problem, a ratio a/σ_{⊥} of the Bohr radius a to the beam width σ_{⊥}, is no longer vanishing. We predict an azimuthal asymmetry of the scattered electrons, which is found to be up to 10%, and argue that it can be reliably detected. The production of beams with the not-everywhere-positive Wigner functions and the probing of such quantum effects can open new perspectives for noninvasive electron microscopy, quantum tomography, particle physics, and so forth.
Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays everywhere positive, which obscures such quantum phenomena as non-locality and entanglement. With the advent of the modern electron microscopes with subnanometer-sized beams one can enter the genuinely quantum regime where the latter effects become only moderately attenuated. Here we show how to probe negative values of the Wigner function in scattering of a coherent superposition of two Gaussian packets with a non-vanishing impact-parameter between them (a Schr\odinger's cat state) by atomic targets. For hydrogen in the ground 1s1s1s state, a small parameter of the problem, a ratio a/σ⊥a/\sigma_{\perp}a/σ⊥​ of the Bohr radius aaa to the beam width σ⊥\sigma_{\perp}σ⊥​, is no longer vanishing. We predict an azimuthal asymmetry of the scattered electrons, which is found to be up to 10%10 \%10% when the impact-parameter is comparable to the beam width, and argue that it can be reliably detected. Production of subnanometer-sized Schr\odinger's cat states and probing such purely quantum effects can open new perspectives in studying the interiors of atoms.
Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum (OAM) and exhibit other features unavailable for plane waves. Collisions of high-energy vortex states can become a promising tool for nuclear and particle physics, once experimental challenges are overcome. An extensive literature exists on scattering processes involving vortex states; however, most works rely on assumptions that will be challenging to achieve in experiment. In this work, we initiate a systematic re-analysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a non-zero impact parameter bbb. Since the total final transverse momentum P⊥P_\perpP⊥​ is no longer fixed, we focus on how the differential cross section depends on P⊥P_\perpP⊥​. We emphasize that non-trivial P⊥P_\perpP⊥​-dependent features can originate either from the shape of the LG wave packets or from the dynamics of the scattering process under interest. Here, we focus on the former source and explore in detail these universal kinematic features, while the study of process-specific modifications, along with the novel insights they may bring, is delegated to a future work. Interestingly, the non-zero impact parameter bbb plays a key role in many P⊥P_\perpP⊥​-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.
Recent theoretical and experimental developments in the field of electron-vortex-beam physics have raised questions about what exactly this novelty in the field of electron microscopy (and other fields, such as particle physics) really provides. An important part of the answer to these questions lies in scattering theory. The present investigation explores various aspects of inelastic quantum scattering theory for cylindrically symmetric beams with orbital angular momentum. The model system of Coulomb scattering on a hydrogen atom provides the setting to address various open questions: How is momentum transferred? Do vortex beams selectively excite atoms, and how can one employ vortex beams to detect magnetic transitions? The analytical approach presented here provides answers to these questions. OAM transfer is possible, but not through selective excitation; rather, by pre- and postselection one can filter out the relevant contributions to a specific signal.
Angular momentum plays a central role in quantum mechanics, recurring in every length scale from the microscopic interactions of light and matter to the macroscopic behavior of superfluids. Vortex beams, carrying intrinsic orbital angular momentum (OAM), are now regularly generated with elementary particles such as photons and electrons. Thus far, the creation of a vortex beam of a nonelementary particle has never been demonstrated experimentally. We present vortex beams of atoms and molecules, formed by diffracting supersonic beams of helium atoms and dimers off transmission gratings. This method is general and could be applied to most atomic and molecular gases. Our results may open new frontiers in atomic physics, using the additional degree of freedom of OAM to probe collisions and alter fundamental interactions.
We explore the elastic scattering of nonrelativistic electrons in the form of Bessel-Gaussian (BG), standard Laguerre-Gaussian (sLG), and elegant Laguerre-Gaussian (eLG) packets on atomic targets in the generalized Born approximation. Scattering by hydrogenlike, iron, silver, and golden targets is considered. The incident electron carries a nonzero orbital angular momentum, while sLG and eLG packets have a definite radial quantum number nnn as well. In the scattering of sLG and eLG wave packets by a macroscopic target, sensitivity of the average cross section to the orbital angular momentum is observed, which is absent for BG packets. We discuss the potential experimental realization of vortex-electron wave packets of these three types. The distinguishing features in the scattering results can be employed for imaging purposes and revelation of the packet properties in experiments.