On the diffraction of dense electron beams in quantum mechanics

Francisco Carlos Lovey

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.

Emil Zolotoyabko

Yujia Yang, Chung-Soo Kim, Richard G. Hobbs +2 more

Semitransparent mirrors are standard elements in light optics for splitting light beams or creating two versions of the same image. Such mirrors do not exist in electron optics, although they could be beneficial in existing techniques such as electron interferometry and holography and could enable alternative electron imaging and spectroscopy techniques. We propose a design for an electron beam splitter using the concept of quantum interaction-free measurement (IFM). The design combines an electron resonator with a weak phase grating. Fast switching gates allow electrons to enter and exit the resonator. While in the resonator, the phase grating transfers intensity from the direct beam into one of the weakly diffracted beams at each pass. To make the beam splitter an efficient two-port splitter, the intensity in all other diffracted beams is blocked by an aperture. The IFM principle minimizes the loss of total intensity by this aperture. We use a scattering matrix method to analyze the performance of the beam splitter, including the effects of inelastic scattering in the phase grating. This design can be generalized to beam splitters for not only electrons, but also photons, neutrons, atoms, and other quantum mechanical systems.

Ilja Rückmann, K. Jarašiūnas, Eugenijus Gaubas

Abstract Transient light‐induced gratings due to free carriers and excitons are created in CdSe in a medium density range of 1015 to 1017 cm−3 by two coherent intense (ns) IR‐pump beams. Detailed investigations of probe‐beam diffraction due to thin excitonic gratings in the spectral region just below the An = 1 ‐exciton line at 85 K and its dependence on sample temperature and on the excitation level are presented. First‐order diffraction efficiences up to 5% and a nonlinear dependence of diffraction on the excitation level can be observed. For the first time numerical calculations of probe‐beam diffraction due to excitonic phase and amplitude gratings are presented. The comparison with the experiment shows, that the damping of a dense exciton gas increases proportional to the excitation intensity in the case of two‐photon interband excitation, and that the light‐induced absorptive changes Δ due to dense excitons dominate over the dispersive changes Δn in the spectral region under consideration.

D. C. Glattli