Electron Interferometry

Massive-particle interferometry can provide tests of fundamental ideas in quantum mechanics, due to the presence of mass and charge, not possible with the more familiar optical interferometry. Most importantly, since the first observation of electron diffraction in 1927 by Davisson, Germer and Thomson [1] (and the observation of electron Fresnel edge fringes by Boersch in 1940 [2]), it has been clear that matter diffracts, according to de Broglie's 1924 hypothesis. (► Davisson-Germer Experiment) The subsequent demonstration of Young's pinhole and biprism experiments (discussed below) with ► electrons about fifty years ago has since led to astonishing demonstrations of, for example, the diffraction of beams of buckyballs by a grating [3] and effects of gravity on neutron interferometry [4]. For neutrons and electrons, both Fermions, new effects due to ► spin and the ► exclusion principle might also be expected, not seen with photons (► light quantum). Perhaps the most famous experiments to date have been tests of the ► Aharonov-Bohm effect using electrons, and those using neutrons to see the effects of gravity on interference, but there have been many more (including an electron Sagnac interferometer and experiments on ► decoherence). The separate but closely related field of electron holography has come to prominence in recent decades, with applications in materials science and superconducting vortex imaging. Here we briefly review work on electron interferometry, first reviewed at an early stage by Denis Gabor [5], and also provide some guidance to the rapidly growing contemporary electron holography literature. Historically, it is of interest to note that the analysis of multiple scattering, and the role of the mean inner potential, in the experiments of Davisson and Germer by H. Bethe in his thesis work introduced Floquet's theorem into condensed matter physics for periodic structures, leading to the review article which founded modern condensed matter physics [6]. Bethe and Bloch were both students of A. Sommerfeldin 1928.

The construction of an electron interferometer requires a beam-splitter and a small, bright source of electrons. This should be of sufficiently small size d _s to produce a spatial coherence width L _c which spans the beam-splitter. (L _c ~ λ/Θ_c for a source at distance L & d _s/(2Θ_c) from the beamsplitter). Prior to the development of the field-emission electron source in 1968 [7] the use of heated tungsten wire pointed filaments produced values of L _c < 1 micrometer, so that early workers understood the need for an extremely small beamsplitting device, which limited development of the field. But even before the peak of interest in the Aharonov-Bohm effect in the 1960s, both amplitude and wavefront dividing beamsplitters had been demonstrated for electron beams. The first, using Bragg scattering [8], has since been abandoned in favor of the Mollenstedt and Duker electrostatic biprism, which may be said to have founded the field of electron interferometry [9].