Fluctuations in the counting rate of photons originating from uncorrelated point sources become, within the coherently illuminated area, slightly enhanced compared to a random sequence of classical particles. This phenomenon, known in astronomy as the Hanbury Brown-Twiss effect, is a consequence of quantum interference between two indistinguishable photons and Bose Einstein statistics. The latter require that the composite bosonic wavefunction is a symmetric superposition of the two possible paths. For fermions, the corresponding two-particle wavefunction is antisymmetric: this excludes overlapping wave trains, which are forbidden by the Pauli exclusion principle. Here we use an electron field emitter to coherently illuminate two detectors, and find anticorrelations in the arrival times of the free electrons. The particle beam has low degeneracy (about 10(-4) electrons per cell in phase space); as such, our experiment represents the fermionic twin of the Hanbury Brown-Twiss effect for photons.

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 spec...

Controlled decoherence of free electrons due to Coulomb interaction with a truly macroscopic environment, the electron (and phonon) gas inside a semiconducting plate, is studied experimentally. The quantitative results are compared with different theoretical models. The experiment confirms the main features of the theory of decoherence and can be interpreted in terms of which-path information. In contrast to previous model experiments on decoherence, the obtained interferograms directly visualize the transition from quantum to classical.

A Sagnac experiment with electron waves in vacuum is reported. The phase shift caused by rotation of an electron biprism interferometer placed on a turntable has been measured. It was found to agree with prediction within error margins of about 30Fo. A compact ruggedized electron interferometer was used. It is based on a high-precision optical bench of 36-cm length. This interferometer is less sensitive by orders of magnitude to mechanical vibrations and electromagnetic stray fields than conventional electron interferometers. A beam of low-energy electrons (150-3000 eV) emitted by a field-emission electron source was used. For the most part, electrostatic electron optical components were employed. The magnified interference fringe pattern was intensified by a dual-stage multichannel-plate intensifier, recorded by a charge-coupled-device video camera, transmitted from the turntable to the laboratory system via a slip ring, and evaluated by an image-processing system. Both the rotation rate and the area enclosed between the two partial waves were varied (up to values of 0.5 s and 3.9 mm, respectively). Fringe shifts on the order of 5% of a fringe period were attained. Some historical aspects of the Sagnac efFect as well as some aspects of its interpretation are mentioned. A brief informal discussion is included of the interpretation of the Sagnac phase shift as a geometric phase ("Berry phase") caused by the global anholonomy of the local phase factor that is produced by the gauge field induced by rotation.PACS number(s): 03.65. Bz, 03.30. +p, 06.30.Gv, 41.90.+e

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