Progress in electron- and ion-interferometry

In the 1970s the prominent goal was to overcome the limitations of electron microscopy caused by aberrations of electron lenses by the development of electron holography. In the meantime this problem has been solved, not only in the roundabout way of holography, but directly by correcting the aberrations of the lenses. Nevertheless, many quantitative electron microscopical measurement methods—e.g. mapping and visualization of electric and magnetic fields—were developed within the context of holography and have become fields of their own. In this review we focus on less popular electron interferometric experiments which complement the field of electron holography. The paper is organized as follows. After a short sketch of the development of electron biprism interferometry after its invention in 1954, recent advances in technology are discussed that made electron biprism interferometry an indispensable tool for solving fundamental and applied questions in physics: the development and preparation of conventional and single-atom field electron and field ion sources with their extraordinary properties. Single- and few-atom sources exhibit spectacular features: their brightness at 100 keV exceeds that of conventional field emitters by two orders in magnitude. Due to the extremely small aberrations of diode field emitter extraction optics, the virtual source size of single-atom tips is on the order of 0.2 nm. As a consequence it illuminates an area 7 cm in diameter on a screen at a distance of 15 cm coherently. Projection electron micrographs taken with these sources reach spatial resolutions of atomic dimensions and in-line holograms are—due to the absence of lenses with their aberrations—not blurred. Their reconstruction is straightforward. By addition of a carbon nanotube biprism into the beam path of a projection microscope a lensless electron interferometer has been realized. In extremely ultrahigh vacuum systems flicker noise is practically absent in the new sources. In the context of holography, methods have been developed to record holograms without modulation of the biprism fringes by waves diffracted at the edges of the biprism filament. This simplifies the reconstruction of holograms and the evaluation of interferograms (taken, e.g. to extract a spectrum by Fourier analysis of the fringe system) significantly. A major section is devoted to the influence of electromagnetic and gravito-inertial potentials and fields on the quantum mechanical phase of matter waves: the Aharonov–Bohm effect, the inertial Aharonov–Bohm effect and its realization, the Sagnac effect and Sagnac experiments with atoms, superfluid helium, Bose–Einstein condensates, electrons and ions and their potential as rotation sensors are discussed. Möllenstedt and Wohland discovered in a crossed beam analyzer (Wien filter) an optical element for charged particles that shifts wave packets longitudinally that transverse a Wien filter on laterally separated paths. This new optical element rendered it possible to measure coherence lengths and the spectrum of charged particle waves by visibility- and Fourier-spectroscopy, to perform a 'Welcher Weg' experiment, to re-establish seemingly lost longitudinal coherence in an interferometer for charged particles and to realize a decoherence free quantum eraser. A precision test of decoherence according to a proposal from Anglin and Zurek and biprism interferences with helium atoms close the section on first-order coherence experiments. The topics of the last section are Hanbury Brown–Twiss correlations and an antibuching experiment of free electrons.