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

arXiv:1302.2936 · Physical Review E

Scattering of quantum wave packets by shallow potential islands: A quantum lens

Arseni Goussev, Klaus Richter

Published May 28, 2013• 3 citations
arXivHTMLPDF

Abstract

We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics.

DOI
10.1103/physreve.87.052918

Related papers

Nonstationary theory of wave-packet potential scattering

Dmitri Bitouk, Mikhail Vladimirovich Fedorov

Potential scattering of free-electron wave packets is considered in the framework of the nonstationary quantum-mechanical theory. To characterize the efficiency of this process, the average angle of scattering is calculated in the lowest (first and second) orders of perturbation theory in the potential. In the approximation of a well-localized, narrow, and nonspreading wave packet, the first-order term is shown to agree with the classical angle of scattering, linear in the potential. This term is shown to vanish at a very large size of the initial wave packet (much larger than the size of a target). An analogy between the potential scattering of wave packets and electron-light ponderomotive scattering is discussed.

Physical Review A•Aug 1, 1998•4 citations

Classical properties of quantum scattering

Władysław Żakowicz

Quantum elastic potential scattering of a particle is re-examined taking into account exact solutions of the corresponding Schrödinger equation. In addition to the scattering of stationary plane waves and stationary finite-width wave beams, nonstationary wave packets having finite duration times are studied and some corresponding examples are presented. The role of interference between the scattered wave and the advancing incident beam is studied. Several two-dimensional scattering problems, involving axially symmetric, generic examples of nonuniform attractive and repulsive potentials, are discussed in more detail. This discussion concentrates on finding proper conditions when the solutions of the Schrödinger equation may resemble the corresponding solutions of the classical Newton equation. Examples are shown where such similarities occur.

Journal of Physics A Mathematical and General•Apr 2, 2003•7 citations

Wave Packet Dynamics on Two-Dimensional Quadratic Potential Surfaces

Attila Aşkar, Jerome H. Weiner

Computer-generated figures within the framework of the hydrodynamic analogy to the time-dependent Schrödinger equation are presented for the motion of Gaussian wave packets on two-dimensional potential surfaces. The three cases treated illustrate (a) motion in a potential well, (b) tunneling through a saddle point, and (c) scattering by a potential barrier.

American Journal of Physics•Oct 1, 1971•26 citations

Coherent multiple scattering: from atomic matter waves to light and vice versa

Nicolas Cherroret

This manuscript presents a selection of works on the coherent evolution of atomic matter waves in random potentials. In this context, a number of interference, « mesoscopic » phenomena surviving a disorder average are discussed, in particular in the regime where Anderson localization shows up: coherent backscattering, coherent forward scattering, mesoscopic echo and quantum boomerang effect. The interplay between weak atomic interactions and Anderson localization is also touched upon for spreading wave packets, a scenario frequently considered in experiments. The last chapter, finally, gives an overview of recent works by the author on multiple scattering of light in media of dimension « (2+1) ». These peculiar systems, originally introduced to demonstrate Anderson localization of light in 2D, have sparked a growing interest in the recent years, for light propagation is governed by an effective Schrödinger equation and thus mimics the behavior of a matter wave. We here show that when the vector character of light is properly taken into account, these systems in fact display a physics much richer than the one pertained to this sole analogy.

•Nov 14, 2018•1 citation

Interfacing light and single atoms with a lens

Meng Khoon Tey, Syed Abdullah Aljunid, Florian Huber +4 more

Abstract. We investigate the interaction between a single atom and a light field in the strong focusing regime. Such a configuration is subject to recent experimental work not only with atoms but also molecules and other atom-like systems as quantum dots. We derive the scattering probability for a photon from such a microscopic object modeled by a two-level system, starting with a Gaussian beam as the spatial mode of the light field. The focusing by an ideal lens is modeled using spherical wave fronts of a field compatible with Maxwell equations. Using a semi-classical approach for the atom-field interaction, we predict scattering probability of photons by a single atom of up to 98% for realistic focusing parameters. Experimental results for different focusing strengths are compared with our theoretical model. PACS numbers: 42.50Ct, 42.50Ex, 42.25BsInterfacing light and single atoms with a lens 2 1.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 2, 2008•7 citations

A trajectory-based understanding of quantum interference

Ángel S. Sanz, Salvador Miret-Artés

Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical perspective and the Bohmian one. From this analysis, clear and insightful pictures of the physics involved in these kind of processes are obtained, which are of general validity (i.e., regardless of the type of wave packets considered) in the understanding of more complex cases where interference is crucial (e.g., scattering problems, slit diffraction, quantum control scenarios or, even, multipartite interactions). In particular, we show how problems involving wave-packet interference can be mapped onto problems of wave packets scattered off potential barriers.

arXiv:0806.2105•Journal of Physics A Mathematical and Theoretical•Sep 30, 2008•104 citations
We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics.
Potential scattering of free-electron wave packets is considered in the framework of the nonstationary quantum-mechanical theory. To characterize the efficiency of this process, the average angle of scattering is calculated in the lowest (first and second) orders of perturbation theory in the potential. In the approximation of a well-localized, narrow, and nonspreading wave packet, the first-order term is shown to agree with the classical angle of scattering, linear in the potential. This term is shown to vanish at a very large size of the initial wave packet (much larger than the size of a target). An analogy between the potential scattering of wave packets and electron-light ponderomotive scattering is discussed.
Quantum elastic potential scattering of a particle is re-examined taking into account exact solutions of the corresponding Schrödinger equation. In addition to the scattering of stationary plane waves and stationary finite-width wave beams, nonstationary wave packets having finite duration times are studied and some corresponding examples are presented. The role of interference between the scattered wave and the advancing incident beam is studied. Several two-dimensional scattering problems, involving axially symmetric, generic examples of nonuniform attractive and repulsive potentials, are discussed in more detail. This discussion concentrates on finding proper conditions when the solutions of the Schrödinger equation may resemble the corresponding solutions of the classical Newton equation. Examples are shown where such similarities occur.
This manuscript presents a selection of works on the coherent evolution of atomic matter waves in random potentials. In this context, a number of interference, « mesoscopic » phenomena surviving a disorder average are discussed, in particular in the regime where Anderson localization shows up: coherent backscattering, coherent forward scattering, mesoscopic echo and quantum boomerang effect. The interplay between weak atomic interactions and Anderson localization is also touched upon for spreading wave packets, a scenario frequently considered in experiments. The last chapter, finally, gives an overview of recent works by the author on multiple scattering of light in media of dimension « (2+1) ». These peculiar systems, originally introduced to demonstrate Anderson localization of light in 2D, have sparked a growing interest in the recent years, for light propagation is governed by an effective Schrödinger equation and thus mimics the behavior of a matter wave. We here show that when the vector character of light is properly taken into account, these systems in fact display a physics much richer than the one pertained to this sole analogy.
Abstract. We investigate the interaction between a single atom and a light field in the strong focusing regime. Such a configuration is subject to recent experimental work not only with atoms but also molecules and other atom-like systems as quantum dots. We derive the scattering probability for a photon from such a microscopic object modeled by a two-level system, starting with a Gaussian beam as the spatial mode of the light field. The focusing by an ideal lens is modeled using spherical wave fronts of a field compatible with Maxwell equations. Using a semi-classical approach for the atom-field interaction, we predict scattering probability of photons by a single atom of up to 98% for realistic focusing parameters. Experimental results for different focusing strengths are compared with our theoretical model. PACS numbers: 42.50Ct, 42.50Ex, 42.25BsInterfacing light and single atoms with a lens 2 1.
Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical perspective and the Bohmian one. From this analysis, clear and insightful pictures of the physics involved in these kind of processes are obtained, which are of general validity (i.e., regardless of the type of wave packets considered) in the understanding of more complex cases where interference is crucial (e.g., scattering problems, slit diffraction, quantum control scenarios or, even, multipartite interactions). In particular, we show how problems involving wave-packet interference can be mapped onto problems of wave packets scattered off potential barriers.