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

Abstract

We theoretically demonstrate the feasibility of producing electron beam splitter using Kapitza-Dirac diffraction on bichromatic standing waves which are created by the fundamental frequency and the third harmonic. The relativistic electron in Bragg regime absorbs three photons with frequency of ω and emits a photon with frequency of 3ω, 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 Rabi oscillation between initial and scattered states is changed and finds two unequal peaks. In circular polarization for fundamental and third harmonic, despite Rabi oscillation, the spin down electron in 0.56 fs intervals maintains its momentum and spin. Also we present an electron spin filter with combination of a linearly polarized fundamental laser beam and a third harmonic with circular polarization that scatters the electron beam according to its spin state.

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

“…The optical regime has the advantage that the classical nonlinearity parameter ξ = qA/m can reach values of 1 with comparably low effort, such that high photon number Kapitza-Dirac scattering, as for example discussed in references [39,40,[44][45][46][47][49][50][51]] could be possible.…”

“…In the context of electron diffraction in standing light waves we refer to strong interactions when the final diffraction pattern shows many diffraction peaks (diffraction regime) and a weak interaction when the final diffraction pattern only shows a Bragg peak (Bragg regime) [35,36]. Spin effects [37][38][39][40][41][42][43][44][45] and also spin-dependent diffraction [46][47][48][49][50] (ie. sorting of electrons according to their spin state) has been discussed theoretically for the Kapitza-Dirac effect.…”

“…sorting of electrons according to their spin state) has been discussed theoretically for the Kapitza-Dirac effect. While the original proposal from Kapitza and Dirac considers a two-photon momentum transfer, higher order photon scattering is possible [39,40,[44][45][46][47][49][50][51] but might be suppressed for the case of a weak ponderomotive amplitude of the standing wave light field in the Bragg regime. Therefore, possible implementation difficulties of spindependent electron diffraction could arise for the case of a higher number of interacting photons or the necessity to wait for larger fractions of a Rabi cycle of the electron quantum state transition, which could hinder the observation of such higher order photon interactions.…”

Time evolution of charged particle wave functions in optical crystal: The coherent Kapitza-Dirac effect for plasma-based proton beams

“…The effect of the strength and orientations of external perturbations such as electric and magnetic fields on the coherently split proton beams will be interesting to study experimentally. Through the use of an optical crystal, it may provide answers to questions such as whether a change in the orientation of the spin in a proton beam will have any effect on the diffraction pattern; this will belong to another area of physics that can be investigated [42,45,46]. The probability to detect a particle in mth order diffraction peak is given by [47],…”

“…KD effect continues to be a subject of active research and finds wide applications in areas such as matter-wave interferometers [28], general relativity [29][30][31][32], gravitational waves [33][34][35][36][37][38][39], determination of fine structure constant [40,41] including non-perturbative quantum dynamical systems [41]. It has been demonstrated recently that the KD effect on optical standing waves formed by the fundamental frequency and it's third harmonic can be used as an electron beam splitter [42]. Spin flips in the Compton scattering during the interaction with optical crystal has been studied by D. Seipt et al(2018) [43] using the density matrix formalism.…”