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Physical Review A

Feasibility of observing two-electron interference

Tetsuji Kodama, Nobuyuki Osakabe, Junji Endo, Akira Tonomura, Kohji Ohbayashi, Tsuneyuki Urakami, Shinji Ohsuka, Hiroshi Tsuchiya, Yutaka Tsuchiya, Y. Uchikawa

Published Apr 1, 1998• 26 citations
Publisher

Abstract

The feasibility of observing two-electron interference is considered. The detection of antibunching in an intensity cross-correlation function using coincidence-delay measurement would be the most feasible experiment. The data acquisition time to observe electron antibunching in a coherent field-emission beam is estimated by taking into account the transversal coherence with a possible experimental configuration. With the available measurement system in an optimized condition, the data acquisition time is found to be $\ensuremath{\sim}{10}^{2}$ h, being considered to be the permissible duration of measurement time.

DOI
10.1103/physreva.57.2781

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The feasibility of observing two-electron interference is considered. The detection of antibunching in an intensity cross-correlation function using coincidence-delay measurement would be the most feasible experiment. The data acquisition time to observe electron antibunching in a coherent field-emission beam is estimated by taking into account the transversal coherence with a possible experimental configuration. With the available measurement system in an optimized condition, the data acquisition time is found to be \ensuremath∼102\ensuremath{\sim}{10}^{2}\ensuremath∼102 h, being considered to be the permissible duration of measurement time.
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.
We investigate the intensity interference between pairs of electrons using a spin-polarized electron beam having a high polarization and a narrow energy width. We observe spin-dependent antibunching on the basis of coincident counts of electron pairs performed with a spin-polarized transmission electron microscope, which could control the spin-polarization without any changes in the electron optics. The experimental results show that the time correlation was only affected by the spin polarization, demonstrating that the antibunching is associated with fermionic statistics. The coherent spin-polarized electron beam facilitates the extraction of intrinsic quantum interference.
We consider temporally integrating interferometric measurements and their relation to the coherence properties of nonstationary light. We find that performing such experiments as a function of time delay is equivalent to spectrally resolving the interference patterns, and time-domain coherence information can be obtained from field autocorrelation only if the source is of the Schell-model type. In an analogy to autocorrelation, we introduce field cross-correlation, which can be used to determine the complete complex field of unknown signal pulses if suitable probe pulses are available. We demonstrate our findings with simulated supercontinuum and free-electron laser ensembles, and discuss the prospect of carrying out experiments.
For a continuous beam, particles that arrive at random times show a flat second-order correlation function, g(2), as measured by a flat coincidence spectrum. A reduction in the likelihood for two particles in such a continuous beam to arrive at the same time is called antibunching, observed as a dip in the otherwise flat coincidence spectrum. For a pulsed beam, the coincidence spectrum consists of a series of equal height peaks, where the "dip" manifests as a reduction in the height of the zero-delay time peak. For electrons, such a dip is an experimental signature of Coulomb repulsion and Pauli pressure. This paper discusses another effect that can produce a similar signature but that does not originate from the properties of the physical system under scrutiny. Instead, the detectors and electronics used to measure those coincidences suffer significantly even from weak crosstalk. A simple model that explains our experimental observations is given. Furthermore, we provide an experimental approach to correct this type of crosstalk.
Advanced electron microscopy technologies have made it possible to perform precise double-slit interference experiments. We used a 1.2-MV field emission electron microscope providing coherent electron waves and a direct detection camera system enabling single-electron detections at a sub-second exposure time. We developed a method to perform the interference experiment by using an asymmetric double-slit fabricated by a focused ion beam instrument and by operating the microscope under a "pre-Fraunhofer" condition, different from the Fraunhofer condition of conventional double-slit experiments. Here, pre-Fraunhofer condition means that each single-slit observation was performed under the Fraunhofer condition, while the double-slit observations were performed under the Fresnel condition. The interference experiments with each single slit and with the asymmetric double slit were carried out under two different electron dose conditions: high-dose for calculation of electron probability distribution and low-dose for each single electron distribution. Finally, we exemplified the distribution of single electrons by color-coding according to the above three types of experiments as a composite image.
Correlations between successive detections in beams of free electrons are studied with a transmission electron microscope. For incoherent illumination of the detectors, a certain random coincidence probability is observed, indicative for uncorrelated arrival times of the electrons. When the illumination is changed from incoherent to coherent, a reduction of the random coincidence probability is observed, indicative for antibunching in the arrival times of the electrons. However, the amount of reduction is larger than the theoretically expected value calculated from the Pauli principle, forbidding more than one identical fermion to occupy the same quantum state. For a certain coherent illumination of the detectors, where we use magnetic lenses in electron microscopes for magnifications of the coherence length, we find an enhanced coincidence probability, indicative for bunching in the arrival times of the electrons. This originates from correlations in beams of free electrons due to Coulomb interactions.