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:1604.06201 · Physical Review A

Electron-spin filter and polarizer in a standing light wave

Sven Ahrens

Published Nov 30, 2017• 15 citations
arXivHTMLPDF

Abstract

We demonstrate the theoretical feasibility of spin-dependent diffraction and spin polarization of an electron in two counterpropagating, circularly polarized laser beams. The spin dynamics appears in a two-photon process of the Kapitza-Dirac effect in the Bragg regime. We show the spin dependence of the diffraction process by comparison of the time evolution of spin-up and spin-down electrons in a relativistic quantum simulation. We further discuss the spin properties of the scattering by studying an analytically approximated solution of the time-evolution matrix. A classification scheme in terms of unitary or nonunitary propagation matrices is used for establishing a generalized and spin-independent description of the spin properties in the diffraction process.

DOI
10.1103/physreva.96.052132

Related papers

Spin-dependent two-photon Bragg scattering in the Kapitza-Dirac effect

Sven Ahrens, Zhenfeng Liang, Tilen Čadež +1 more

We present the possibility of spin-dependent Kapitza-Dirac scattering based on a two-photon interaction only. The interaction scheme is inspired from a Compton scattering process, for which we explicitly show the mathematical correspondence to the spin dynamics of an electron diffraction process in a standing light wave. The spin effect has the advantage that it already appears in a Bragg scattering setup with arbitrary low field amplitudes, for which we have estimated the diffraction count rate in a realistic experimental setup at available x-ray free-electron laser facilities.

arXiv:2001.10177•Physical Review A•Sep 9, 2020•11 citations

Investigation of the Kapitza-Dirac effect in the relativistic regime

Sven Ahrens

Quantum mechanical diffraction is of particular interest, because it contradicts our everyday life experience. \nThis theoretical work considers the diffraction of electrons at standing waves of light, referred \nto as the Kapitza-Dirac effect. The work focuses on a special version of a Kapitza-Dirac effect in which \nthe electron interacts with three photons. The particular property of this 3-photon Kapitza-Dirac effect \nis, that the electron spin is rotated. \nThis work considers different relativistic and non-relativistic quantum mechanical wave equations \nwhich are described in momentum space. On one hand, the quantum dynamics of the diffracted electrons \nis solved numerically in momentum space and the properties of the 3-photon Kapitza-Dirac effect \nare investigated in detail. On the other hand, the quantum dynamics is solved via time-dependent \nperturbation theory and is compared with the numerical results. \nIn contrast to the originally proposed Kapitza-Dirac effect with two interacting photons, the number \nof absorbed and emitted photons by the electron is not equal for the 3-photon Kapitza-Dirac effect. \nTherefore, the diffraction process only appears for relativistic electron momenta in laser propagation \ndirection. Furthermore, a very high field strength of the laser beam is required for driving the Kapitza- \nDirac effect with a measurable diffraction probability. The electron spin is rotated along the axis of the \nmagnetic field of the laser beam, when it undergoes the diffraction process. The rotation angle of the \nspin rotation depends on the electron momentum component in laser polarization direction. Therefore, \nthe probability for flipping the electron spin can be tuned by choosing the electron momentum in \nthe direction of the laser polarization. An experimental investigation may by established by utilizing \nfuture X-ray laser facilities.

•Jan 1, 2012•7 citations

Spin effects in Kapitza-Dirac scattering at light with elliptical polarization

Rico Erhard, Heiko Bauke

The Kapitza-Dirac effect, which refers to electron scattering at standing light waves, is studied in the Bragg regime with counterpropagating elliptically polarized electromagnetic waves with the same intensity, wavelength, and degree of polarization for two different setups. In the first setup, where the electric-field components of the counterpropagating waves have the same sense of rotation, we find distinct spin effects. The spins of the scattered electrons and of the nonscattered electrons, respectively, precess with a frequency that is of the order of the Bragg-reflection Rabi frequency. When the electric-field components of the counterpropagating waves have an opposite sense of rotation, which is the second considered setup, the standing wave has linear polarization, and no spin effects can be observed. Our results are based on numerical solutions of the time-dependent Dirac equation and the analytical solution of a relativistic Pauli equation, which accounts for the leading relativistic effects.

arXiv:1509.01150•Physical Review A•Oct 28, 2015•26 citations

Investigation of electron spin dynamic in the bichromatic Kapitza-Dirac effect via frequency ratio and amplitude of laser beams

Asma Ebadati, Mohsen Vafaee, Babak Shokri

We discuss electron diffraction from two standing waves with two different frequencies. The effects of increasing the frequency of the second laser beam and changing the laser amplitudes on the form and period of the Rabi oscillation are studied theoretically. The corresponding scattering probabilities for certain incident electron momenta are obtained by an analytical Rabi matrix and numerical solution of the Dirac equation. We show that at high intensities, $\ensuremath{\ge}{10}^{20}$ W ${\mathrm{cm}}^{\ensuremath{-}2}$, the process with an even number of photons involved in the Kapitza-Dirac effect can be used as a spin filter for free electrons. On the other hand, the process with an odd number photons and an electron with momentum along the laser polarization preserves the initial spin of the electron.

Physical Review A•Nov 27, 2019•4 citations

Four-photon Kapitza-Dirac effect as an electron spin filter

Asma Ebadati, Mohsen Vafaee, Babak Shokri

We theoretically demonstrate the feasibility of producing an electron spin beam splitter using Kapitza-Dirac diffraction on bichromatic standing waves which are created by the fundamental frequency and its third harmonic. The relativistic electron in the Bragg regime absorbs three photons with a frequency of $\ensuremath{\omega}$ and emits a photon with a frequency of $3\ensuremath{\omega}$; we introduce this as the four-photon Kapitza-Dirac effect. In this four-photon Kapitza-Dirac effect distinct spin effects arise in different polarizations of the third harmonic laser beam. It is shown that the shape of the Rabi oscillation between the initial and scattered states is changed and finds two unequal peaks for all polarizations of laser beams. For the case of circular polarization of the fundamental and third harmonic, despite Rabi oscillation, the spin down electron beam in 0.23 fs intervals maintains its momentum and spin. Also we find that if a suitable combination of a linearly polarized fundamental laser beam and a third harmonic with circular polarization in the condition $\stackrel{P\vec}{p}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{A}$ term is involved, it results in a spin-dependent oscillation that preserves the spin state of the initial electron.

arXiv:1803.02748•Physical Review A•Sep 17, 2018•8 citations

Parameter-space investigation for spin-dependent electron diffraction in the Kapitza-Dirac effect

Yang Wang, Sven Ahrens

We demonstrate that spin-dependent electron diffraction is possible for a smooth range of transverse electron momenta in a two-photon Bragg scattering scenario of the Kapitza-Dirac effect. Our analysis is rendered possible by introducing a generalized specification for quantifying spin-dependent diffraction, yielding an optimization problem which is solved by making use of a Newton gradient iteration scheme. With this procedure, we investigate the spin-dependent effect for different transverse electron momenta and different laser polarizations of the standing-light-wave Kapitza-Dirac scattering. The possibility of using arbitrarily low transverse electron momenta when setting up a spin-dependent Kapitza-Dirac experiment allows longer interaction times of the electron with the laser and therefore enables less constraining parameters for an implementation of the effect.

arXiv:2308.13200•Physical Review A•Jan 16, 2024•2 citations
We demonstrate the theoretical feasibility of spin-dependent diffraction and spin polarization of an electron in two counterpropagating, circularly polarized laser beams. The spin dynamics appears in a two-photon process of the Kapitza-Dirac effect in the Bragg regime. We show the spin dependence of the diffraction process by comparison of the time evolution of spin-up and spin-down electrons in a relativistic quantum simulation. We further discuss the spin properties of the scattering by studying an analytically approximated solution of the time-evolution matrix. A classification scheme in terms of unitary or nonunitary propagation matrices is used for establishing a generalized and spin-independent description of the spin properties in the diffraction process.
We present the possibility of spin-dependent Kapitza-Dirac scattering based on a two-photon interaction only. The interaction scheme is inspired from a Compton scattering process, for which we explicitly show the mathematical correspondence to the spin dynamics of an electron diffraction process in a standing light wave. The spin effect has the advantage that it already appears in a Bragg scattering setup with arbitrary low field amplitudes, for which we have estimated the diffraction count rate in a realistic experimental setup at available x-ray free-electron laser facilities.
Quantum mechanical diffraction is of particular interest, because it contradicts our everyday life experience. \nThis theoretical work considers the diffraction of electrons at standing waves of light, referred \nto as the Kapitza-Dirac effect. The work focuses on a special version of a Kapitza-Dirac effect in which \nthe electron interacts with three photons. The particular property of this 3-photon Kapitza-Dirac effect \nis, that the electron spin is rotated. \nThis work considers different relativistic and non-relativistic quantum mechanical wave equations \nwhich are described in momentum space. On one hand, the quantum dynamics of the diffracted electrons \nis solved numerically in momentum space and the properties of the 3-photon Kapitza-Dirac effect \nare investigated in detail. On the other hand, the quantum dynamics is solved via time-dependent \nperturbation theory and is compared with the numerical results. \nIn contrast to the originally proposed Kapitza-Dirac effect with two interacting photons, the number \nof absorbed and emitted photons by the electron is not equal for the 3-photon Kapitza-Dirac effect. \nTherefore, the diffraction process only appears for relativistic electron momenta in laser propagation \ndirection. Furthermore, a very high field strength of the laser beam is required for driving the Kapitza- \nDirac effect with a measurable diffraction probability. The electron spin is rotated along the axis of the \nmagnetic field of the laser beam, when it undergoes the diffraction process. The rotation angle of the \nspin rotation depends on the electron momentum component in laser polarization direction. Therefore, \nthe probability for flipping the electron spin can be tuned by choosing the electron momentum in \nthe direction of the laser polarization. An experimental investigation may by established by utilizing \nfuture X-ray laser facilities.
The Kapitza-Dirac effect, which refers to electron scattering at standing light waves, is studied in the Bragg regime with counterpropagating elliptically polarized electromagnetic waves with the same intensity, wavelength, and degree of polarization for two different setups. In the first setup, where the electric-field components of the counterpropagating waves have the same sense of rotation, we find distinct spin effects. The spins of the scattered electrons and of the nonscattered electrons, respectively, precess with a frequency that is of the order of the Bragg-reflection Rabi frequency. When the electric-field components of the counterpropagating waves have an opposite sense of rotation, which is the second considered setup, the standing wave has linear polarization, and no spin effects can be observed. Our results are based on numerical solutions of the time-dependent Dirac equation and the analytical solution of a relativistic Pauli equation, which accounts for the leading relativistic effects.
We discuss electron diffraction from two standing waves with two different frequencies. The effects of increasing the frequency of the second laser beam and changing the laser amplitudes on the form and period of the Rabi oscillation are studied theoretically. The corresponding scattering probabilities for certain incident electron momenta are obtained by an analytical Rabi matrix and numerical solution of the Dirac equation. We show that at high intensities, $\ensuremath{\ge}{10}^{20}$ W ${\mathrm{cm}}^{\ensuremath{-}2}$, the process with an even number of photons involved in the Kapitza-Dirac effect can be used as a spin filter for free electrons. On the other hand, the process with an odd number photons and an electron with momentum along the laser polarization preserves the initial spin of the electron.
We theoretically demonstrate the feasibility of producing an electron spin beam splitter using Kapitza-Dirac diffraction on bichromatic standing waves which are created by the fundamental frequency and its third harmonic. The relativistic electron in the Bragg regime absorbs three photons with a frequency of $\ensuremath{\omega}$ and emits a photon with a frequency of $3\ensuremath{\omega}$; we introduce this as the four-photon Kapitza-Dirac effect. In this four-photon Kapitza-Dirac effect distinct spin effects arise in different polarizations of the third harmonic laser beam. It is shown that the shape of the Rabi oscillation between the initial and scattered states is changed and finds two unequal peaks for all polarizations of laser beams. For the case of circular polarization of the fundamental and third harmonic, despite Rabi oscillation, the spin down electron beam in 0.23 fs intervals maintains its momentum and spin. Also we find that if a suitable combination of a linearly polarized fundamental laser beam and a third harmonic with circular polarization in the condition $\stackrel{P\vec}{p}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{A}$ term is involved, it results in a spin-dependent oscillation that preserves the spin state of the initial electron.
We demonstrate that spin-dependent electron diffraction is possible for a smooth range of transverse electron momenta in a two-photon Bragg scattering scenario of the Kapitza-Dirac effect. Our analysis is rendered possible by introducing a generalized specification for quantifying spin-dependent diffraction, yielding an optimization problem which is solved by making use of a Newton gradient iteration scheme. With this procedure, we investigate the spin-dependent effect for different transverse electron momenta and different laser polarizations of the standing-light-wave Kapitza-Dirac scattering. The possibility of using arbitrarily low transverse electron momenta when setting up a spin-dependent Kapitza-Dirac experiment allows longer interaction times of the electron with the laser and therefore enables less constraining parameters for an implementation of the effect.