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arXiv:2507.06703 · Physical Review A

Optimizing the incident electron momentum for resonant few-photon Kapitza-Dirac scattering in bichromatic laser fields

Ingo Elsner, Carsten Müller

Published Aug 21, 2025• 0 citations
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Abstract

Nonrelativistic Kapitza-Dirac scattering of electrons from counterpropagating bichromatic laser waves is studied in the resonant Bragg regime, taking the electron spin into account. We show that the intrinsic field-induced detuning, which arises in the Rabi oscillation dynamics between initial and scattering state of the electron, can be compensated by a suitable adjustment of its incident momentum. Analytical formulas of the optimized electron momentum for spin-dependent three-photon and spin-independent four-photon Kapitza-Dirac scattering are obtained from simplified model systems in reduced dimensionality, which preserve the characteristic properties of the process.

DOI
10.1103/q7tp-p9vd

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A relativistic description of the Kapitza-Dirac effect in the so-called Bragg regime with two and three interacting photons is presented by investigating both numerical and perturbative solutions of the Dirac equation in momentum space. We demonstrate that spin flips can be observed in the two-photon and the three-photon Kapitza-Dirac effects for certain parameters. During the interaction with the laser field the electron's spin is rotated, and we give explicit expressions for the rotation axis and the rotation angle. The off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not exactly fulfilled, is described by a generalized Rabi theory. We also analyze the in-field quantum dynamics as obtained from the numerical solution of the Dirac equation.
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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.