Electrons emitted from single-atom tips are analysed in a model with the tip as a round tubelike constriction. The source creates two-dimensional minimum wavepackets whose temporal evolution agrees well with observed beam divergences. With few-atom tips interference effects may arise due to the electron's non localized emission from several atoms. The phase space density of emitted electrons is around 10 −2 h −3 , and electron-electron correlation experiments become feasible. In ion field emission mode observed beam divergences are dominated by thermal broadening and other effects rather than quantum mechanical principles. Applications include electron interferometers of lower energy and wider beam separation than hitherto in use, as well as proton and possibly other ion interferometers. Highly focused low energy beams could also be produced.
Electrons emitted from single-atom tips are analysed in a model with the tip as a round tubelike constriction. The source creates two-dimensional minimum wavepackets whose temporal evolution agrees well with observed beam divergences. With few-atom tips interference effects may arise due to the electron's non localized emission from several atoms. The phase space density of emitted electrons is around 10 −2 h −3 , and electron-electron correlation experiments become feasible. In ion field emission mode observed beam divergences are dominated by thermal broadening and other effects rather than quantum mechanical principles. Applications include electron interferometers of lower energy and wider beam separation than hitherto in use, as well as proton and possibly other ion interferometers. Highly focused low energy beams could also be produced.
A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements and chip based applications rely on intensive, tunable, coherent sources for free low energy electron matter waves. In most cases, the electrons get field emitted from a metal nanotip where its radius and geometry towards a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 33 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy and sensor technology
A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements, and chip-based applications rely on intensive, tunable, coherent sources for free low-energy electron-matter waves. In most cases, the electrons get field emitted from a metal nanotip, where its radius and geometry toward a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter-wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 6.4 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy, and sensor technology.
In the early 1900s more and more experimental evidence was accumulated indicating that microscopic particles show wave-like properties in certain situations. These particle-wave features are very evident, e.g., in measurements where electrons are diffracted from a double slit to propagate toward a screen where they are detected. Based on the classical averaging of particles discussed in Section 1.2.2, one expects that the double slit only modulates the overall intensity, not the spatial distribution. Experimentally, however, one observes a nearly perfect interference pattern at the screen implying that the electrons exhibit wave averaging features such as discussed in Section 2.1.2. This behavior, originally unexpected for particle beams, persists even if the experiment is repeated such that only one electron at a time passes the double slit before it propagates to the detection screen. Thus, the wave aspect must be an inherent property of individual electrons and not an ensemble effect. Another, independent argument for the failure of classical physics is that the electromagnetic analysis of atoms leads to the conclusion that the negatively charged electron(s) should collapse into the positively charged ion because the electron–ion system loses its energy due to the emission of radiation. As we will see, this problem can be solved by including the wave aspects of particles into the analysis. In particular, as discussed in Section 2.3.3, waves can never be localized to a point without increasing their momentum and energy beyond bounds.
Electron microscopy and diffraction have long been used to study the structure of materials. A recent development is the achievement of ultrafast time resolution using high-repetition rate single electron sources and single-shot many-electron sources. Achieving large coherence lengths under these conditions is challenging due to intrinsic heating mechanisms including inter-particle Coulombic forces. Near-threshold, pulsed photoionization of atoms trapped and cooled with lasers is being investigated as a means to produce intense electron pulses with large intrinsic coherence length due to a low electron temperature. Photo-ionizaton sources are, of course, not an entirely new idea but recent implementations using trapped atoms offer new possibilities. Several properties of electron beams extracted from such ultracold sources have already been investigated, showing in particular that temperatures of a few Kelvin and emittances in the nanometer-radian range can be achieved with tens of thousands electrons per pulse for nanosecond pulse lengths. This can be combined with delicate shaping of the charge distribution to counteract emittance growth due to non-linear self fields. Using ultrafast lasers for the ionization step, shorter electron pulses can be achieved, but an interesting question is whether the concomitant spread in photon energy still allows for low electron temperature. Recent experiments have shown that few-Kelvin temperatures combined with picosecond pulse lengths are indeed possible. It turns out that this can be understood with a classical model for electron trajectories resulting from photoionization. In addition, experimentally observed polarization effects are in general agreement with model results. --------------------------------------------------------------------------------
The interference between quantum amplitude for two electrons, emitted from two source points, to be detected at two detection points, is a direct result of quantum exchange statistics. Such interference is observed in the coincidence probability, compared with that of statistically independent electrons, by computing the time correlation function from the arrival times of the electrons. When the two detectors are separated by a distance less than the coherence length, the coincidence probability is suppressed for electrons (antibunching) due to the Pauli principle, even though they do not interact with each other. However, electrons are charged particles. The Coulomb potential, which governs the scattering of one charged particle by another, is so long ranged. It is obvious that we must consider the Pauli principle and the Coulomb interactions simultaneously. This paper deals with basic experimental and theoretical investigations of the antibunching behavior of electrons in a free beam by considering the Pauli principle and the direct Coulomb interaction between two individual electrons. The experimentally found dependences are described in a model which considers the Coulomb scattering and theoretical values of correlation signals evaluated by analytical calculations agree with those determined by experiment. A study of the time correlation function from the arrival times of the electrons will lead to an understanding of the physical processes that take place in electron guns.
New levels of control over the atomic motion have been attained through the development of the atom laser. The unique properties of these coherent atomic sources open up a wide range of new possibilities in the fields of atom optics and precision measurement. In this article we have discussed the high contrast interference pattern obtained from an atom laser with two output modes of different energies. It should be possible to create a highly complex interference pattern in the output beam of an atom laser by applying a correspondingly tailored radio wave field for output coupling. A novel atom optical manipulation method allowed us to reflect, recapture and focus an atom laser beam. Due to its simplicity and precision the technique is ideally suited for creating an interferometer for the atom laser beam. It seems feasible to split the atom laser beam into two components and recombine it after delaying one of the two components. The resulting interference pattern would reveal the coherence properties of the atom laser beam.