Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Probing negative values of a Wigner function in scattering of Schr\"odinger cats by atoms

Dmitry V. Karlovets, Valeriy G. Serbo

Published May 2, 2017• 0 citations
OpenAlex

Abstract

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 $1s$ state, a small parameter of the problem, a ratio $a/\sigma_{\perp}$ of the Bohr radius $a$ to the beam width $\sigma_{\perp}$, is no longer vanishing. We predict an azimuthal asymmetry of the scattered electrons, which is found to be up to $10 \%$ 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.

Related papers

Possibility to Probe Negative Values of a Wigner Function in Scattering of a Coherent Superposition of Electronic Wave Packets by Atoms

Dmitry V. Karlovets, Valeriy G. Serbo

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.

arXiv:1705.00860•Physical Review Letters•Oct 24, 2017•13 citations

Quantum scattering beyond the plane-wave approximation

Dmitry V. Karlovets

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.

arXiv:1710.09291•Journal of Physics Conference Series•Dec 1, 2017•5 citations

Operational criterion for Wigner function negativity

Paolo Solinas, Beatrice Donelli, Stefano Gherardini

We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes that enable a direct measurement of the WF, and establishes the coherent-state basis as a privileged basis for determining when the WF exhibits negative regions. We show that the absence (presence) of coherent superpositions in the coherent-state basis provides direct information about the positivity (negativity) of the WF. In particular, the absence of such superpositions constitutes a sufficient condition for WF positivity. Although a general proof of necessity remains elusive, we demonstrate that this condition is also necessary in two relevant cases: Schrödinger-cat states and higher-order cat states on a circle. More precisely, for Schrödinger-cat states we establish a necessary and sufficient condition for the positivity of the WF in full generality, whereas for high-order cat states on a circle we derive an analogous condition in the limit of a large number of densely packed coherent states.

quant-pharXiv:2604.20303•Apr 23, 2026•0 citations

Elastic scattering of Airy electron packets on atoms

D. V. Grosman, Nadezhda Sheremet, I. Pavlov +1 more

The problem of elastic scattering of a nonrelativistic electron Airy beam on a hydrogen atom in the ground $1s$ state is considered in the Born approximation. It is demonstrated that the angular dependence of the scattering probability density is, in general, azimuthally asymmetric. When the position of the atom happens to coincide with a minimum of the probability density of the Airy beam, the asymmetric pattern is represented by four separated peaks. We show that this behavior is very sensitive to the precision with which the relative position of the atom and the minima is defined and study how uncertainty in the position can affect observation of the azimuthal asymmetry. Finally, we consider a spatially localized target and discuss the difficulties of observing the asymmetry for targets with sizes exceeding a critical value determined by the beam parameters and by the position of the target center.

arXiv:2211.16534•Physical Review A•Jun 21, 2023•4 citations

On 'Schrödinger's cat' fringes

Valentin L. Gorshenin, Boulat N. Nougmanov, Farit Ya. Khalili

Non-Gaussian quantum states whose Wigner functions can take negative values are important both for fundamental tests of quantum physics and for the quantum information technologies that have been under active development recently.A typical example of a non-Gaussian state is the so-called Schr odinger's cat state.Its very interesting feature is that its `classical' part (two Gaussian maxima) is geometrically separated from the `nonclassical' part (interference fringes).In this paper, several methodological issues related to these fringes are considered.

Physics-Uspekhi•May 1, 2024•1 citation

Scattering-Induced Spin Entanglement and Phase-Space Non-Classicality Driven by Coherent State Superpositions

Sepide Soltani, Ali Mahdifar, Ebrahim Ghanbari-Adivi

Abstract The generation of quantum entanglement through scattering processes is a fundamental mechanism in quantum information science. In this work, we investigate how coherent-state superpositions, represented as spatial Gaussian wave-packet superpositions, modify nonclassical phase-space features and enhance entanglement production during the scattering of a single particle from a localized spin impurity governed by a Heisenberg-type interaction. We construct even and odd superpositions of coherent states and analyze their time evolution using Fourier-space propagation. The corresponding Wigner distributions are computed analytically, revealing os-cillatory interference fringes and negative-valued regions that quantify nonclassicality. Using the nonclassical volume as a metric, we show that increasing the spatial separation between the Gaussian components enhances nonclassicality, eventually saturating at a stable asymptotic maximum. By incorporating these superposed states as incident wave packets, we compute the post-scattering spin entanglement between the reflected particle and the impurity using the negativity measure. Our results demonstrate that the symmetry of the initial coherent-state superposition fundamentally governs the stability of the generated entanglement: while the even superposition exhibits parameter-sensitive, oscillatory entanglement as the wave-packet separation increases, the odd superpo-sition yields a robust, decay-resistant entanglement plateau across all separation scales. These findings highlight the critical role of engineered nonclassical initial states in optimizing scattering-based quantum technologies

•Sep 1, 2026•0 citations
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.
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.
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.
We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes that enable a direct measurement of the WF, and establishes the coherent-state basis as a privileged basis for determining when the WF exhibits negative regions. We show that the absence (presence) of coherent superpositions in the coherent-state basis provides direct information about the positivity (negativity) of the WF. In particular, the absence of such superpositions constitutes a sufficient condition for WF positivity. Although a general proof of necessity remains elusive, we demonstrate that this condition is also necessary in two relevant cases: Schrödinger-cat states and higher-order cat states on a circle. More precisely, for Schrödinger-cat states we establish a necessary and sufficient condition for the positivity of the WF in full generality, whereas for high-order cat states on a circle we derive an analogous condition in the limit of a large number of densely packed coherent states.
The problem of elastic scattering of a nonrelativistic electron Airy beam on a hydrogen atom in the ground 1s1s1s state is considered in the Born approximation. It is demonstrated that the angular dependence of the scattering probability density is, in general, azimuthally asymmetric. When the position of the atom happens to coincide with a minimum of the probability density of the Airy beam, the asymmetric pattern is represented by four separated peaks. We show that this behavior is very sensitive to the precision with which the relative position of the atom and the minima is defined and study how uncertainty in the position can affect observation of the azimuthal asymmetry. Finally, we consider a spatially localized target and discuss the difficulties of observing the asymmetry for targets with sizes exceeding a critical value determined by the beam parameters and by the position of the target center.
Non-Gaussian quantum states whose Wigner functions can take negative values are important both for fundamental tests of quantum physics and for the quantum information technologies that have been under active development recently.A typical example of a non-Gaussian state is the so-called Schr odinger's cat state.Its very interesting feature is that its `classical' part (two Gaussian maxima) is geometrically separated from the `nonclassical' part (interference fringes).In this paper, several methodological issues related to these fringes are considered.
Abstract The generation of quantum entanglement through scattering processes is a fundamental mechanism in quantum information science. In this work, we investigate how coherent-state superpositions, represented as spatial Gaussian wave-packet superpositions, modify nonclassical phase-space features and enhance entanglement production during the scattering of a single particle from a localized spin impurity governed by a Heisenberg-type interaction. We construct even and odd superpositions of coherent states and analyze their time evolution using Fourier-space propagation. The corresponding Wigner distributions are computed analytically, revealing os-cillatory interference fringes and negative-valued regions that quantify nonclassicality. Using the nonclassical volume as a metric, we show that increasing the spatial separation between the Gaussian components enhances nonclassicality, eventually saturating at a stable asymptotic maximum. By incorporating these superposed states as incident wave packets, we compute the post-scattering spin entanglement between the reflected particle and the impurity using the negativity measure. Our results demonstrate that the symmetry of the initial coherent-state superposition fundamentally governs the stability of the generated entanglement: while the even superposition exhibits parameter-sensitive, oscillatory entanglement as the wave-packet separation increases, the odd superpo-sition yields a robust, decay-resistant entanglement plateau across all separation scales. These findings highlight the critical role of engineered nonclassical initial states in optimizing scattering-based quantum technologies