Observation of the Quantum-Classical Transition via Electron Diffraction

Glen Gronniger

The diffraction of electrons by natural crystal structures was first observed in 1927. Before the start of this work, it was not clear whether or not the high quality gratings currently available could be used for electron diffraction due to image charge and other electron grating interactions. We observe for the first time electron diffraction from man made diffraction gratings of 100 nm periodicity. The high quality of diffraction and the ability to "pick" the periodicity allowed us to construct the first Mach-Zehnder electron interferometer using these gratings. Multiple approaches, including a prototype of our current interferometer and the combination of a grating with an electron bi-prism, were unsuccessful. Many stabilization issues must be overcome to observe electron interference fringes in the interferometer. Many experimental design ideas were used to reach proper stabilization requirements. The final interferometer design constructed was the only interferometer to obtain electron interference fringes. The theoretical model used to analyze the data is based on the path integral formalism. This calculates the amplitude associated with all classical paths through the experimental device. The sum of all amplitudes, the path integral, yields the resulting probability at the detection screen. We obtain good fits between our path integral calculations and experimental data. Alternate explanations of our data, such as the possibilities of Talbot Lau and classical Moiré interferometers are ruled out in favor of the Mach-Zehnder explanation. This type of interferometer could be used for future experiments. An experiment for which the fundamental quantum mechanical experiment has never been done; observing the dispersion-less nature of the Aharonov-Bohm Effect, may lend itself to the characteristics of this type of interferometer. Preliminary calculations have been performed to investigate the feasibility of using the grating technology to perform the required experiment.

S. M. Tan, Daniel F. Walls

Ángel S. Sanz, F. Borondo, Salvador Miret-Artés

The method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of atom diffraction by surfaces. As an example, a realistic model for the scattering of He off corrugated Cu is considered. In this way, the final angular distribution of trajectories is obtained by box counting, which is in excellent agreement with the results calculated by standard $S$ matrix methods of scattering theory. More interestingly, the accumulation of quantum trajectories at the different diffraction peaks is explained in terms of the corresponding quantum potential. This nonlocal potential ``guides'' the trajectories causing a transition from a distribution near the surface, which reproduces its shape, to the final diffraction pattern observed in the asymptotic region, far from the diffracting object. These two regimes are homologous to the Fresnel and Fraunhofer regions described in undulatory optics. Finally, the turning points of the quantum trajectories provide a better description of the surface electronic density than the corresponding classical ones, usually employed for this task.

Li Wang, B.-J. Zhang, Z. Hua +3 more

We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.

赵文垒, Jie Quan-Lin, Zhou Shu Bo