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Abstract

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