STM-D-0651Paper2012Settled physics

The Young-Feynman two-slits experiment with single electrons: Build-up of the interference pattern and arrival-time distribution using a fast-readout pixel detector

Stefano Frabboni · Alessandro Gabrielli · Gian Carlo Gazzadi · Filippo Giorgi · Giorgio Matteucci · Giulio Pozzi · Nicola Semprini Cesari · Mauro Villa · Antonio Zoccoli

Abstract and summary · read the original at the source

In one page

The two-slit experiment with single electrons is the one Bohr and Einstein argued over and the one Feynman built his lectures around. As this paper notes, the part that matters most — watching the pattern grow one electron at a time — had only ever been done with an electron biprism, never with real slits. This Modena and Bologna team did it with real slits. They milled two openings about 95 nanometres wide and 430 nanometres apart through a quarter-micron of gold with a focused ion beam, put the sample inside an ordinary transmission electron microscope, and replaced the viewing screen with a silicon pixel chip built for future particle colliders — a chip that records not just where each electron lands but when, at up to a million frames a second. Electrons arrived on average ten milliseconds apart while taking nine nanoseconds to cross the column, so each one was detected and cleared long before the next was emitted. Stack the frames and the interference pattern grows out of the individual dots, one electron at a time.

Why it matters hereChapter 2 holds that empty space is a real medium, and the accounts of interference that take that literally — the zero-point-field trajectory picture at /library/stm-7071935008 among them — have to reproduce exactly this data set: single arrivals, Poisson statistics, and a fringe pattern that only exists in the sum. Chapter 10 gets the instrument. Electron interferometry of this kind is how phase is measured directly, and it is the same bench on which the Aharonov–Bohm effect shows the vector potential shifting fringes where no field touches the electron.

What it claims

01The two slits were made rather than found. A focused ion beam milled two rectangular patterns through a gold layer about 250 nanometres thick, flash-evaporated onto a carbon-coated copper grid, using a 10 picoampere beam with a spot size of about 10 nanometres and monitoring the breakthrough by the change in brightness of the ion-induced secondary electrons. The finished slits are about 95 nanometres wide, 430 nanometres apart and 1550 nanometres long.Section 2, The experimental set-up; Figure 1
Published and peer-reviewed
02The optics are an off-the-shelf electron microscope used as an optical bench. A Philips EM400T with a hairpin filament at 60 kiloelectronvolts gives a de Broglie wavelength of 4.86 picometres; because the slit separation puts the diffraction angles at the order of ten to the minus five radians, the pattern has to be taken in low-angle diffraction mode, with the condensers driven to maximum for lateral coherence and the objective weakly excited, so that the microscope works as a diffraction camera whose camera length can be run up to several hundred metres.Section 2, The experimental set-up
Published and peer-reviewed
03The detector is a collider chip. Apsel4D is a custom monolithic active pixel sensor, a matrix of 128 by 32 pixels of 50 micrometres square in 0.13 micrometre CMOS, designed for the innermost vertex layers of the next generation of particle physics experiments and equipped with a fast digital readout that gives each hit a time stamp. Only hit pixels are read out, unlike a CCD; test runs have shown the chip standing a million frames per second continuously, and the interference data were taken at a conservative 6.25 kilohertz, a 165 microsecond frame period.Section 2, The experimental set-up
Published and peer-reviewed
04The electrons really do arrive one at a time, and the paper measures it rather than assuming it. About 131,000 hit pixels were recorded in roughly 20 minutes; fewer than about one per cent of frames hold more than one electron; and the distribution of intervals between consecutive non-empty frames fits an exponential, confirming a Poisson process, with a slope of 0.09975 plus or minus 0.00040 per millisecond and therefore an average interval between detected electrons of 10.0 milliseconds. The time of flight through the microscope column is 9 nanoseconds, so each electron is completely read out before the next leaves the filament.Section 3, Results; Figures 3 and 4
Settled physics
05The pattern appears only in the sum. Individual frames show single hits and empty frames; adding the stack produces the expected two-slit interference fringes modulated by the diffraction envelope of the individual slit widths, with a fringe spacing that matches the calibrated camera length and the group’s earlier measurements, and a fitted partial coherence of the illumination of 0.6. This is the first time the build-up by single electrons has been observed with a genuine two-slit set-up rather than with an electron biprism, and the authors note two advantages of the slits: the electrons do not interact with the biprism’s electric field, and the images are Fraunhofer patterns, which are far simpler to interpret than the biprism’s Fresnel images.Section 1, Introduction; Section 3, Results; Figure 5; Section 4, Conclusions
Settled physics
06What the authors want to do next. With this much single-electron statistics it becomes possible to study the detailed properties of interference pattern formation, which they tie directly to important tests of quantum mechanics; they also flag the detector’s potential for revealing effects in both static and time-dependent regimes, and note that the experiment ran right at the limit of the microscope’s mechanical stability, with drift visible after 20 minutes.Section 3, Results, closing paragraph; Section 4, Conclusions
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Read it · abstract

Abstract

The two-slits experiment for single electrons has been carried out by inserting in a conventional transmission electron microscope a thick sample with two nano-slits fabricated by Focused Ion Beam technique and a fast recording system able to measure the electron arrival-time. The detector, designed for experiments in future colliders, is based on a custom CMOS chip equipped with a fast readout chain able to manage up to 10⁶ frames per second. In this way, high statistic samples of single electron events can be collected within a time interval short enough to measure the distribution of the electron arrival-times and to observe the build-up of the interference pattern.

Keywords: matter waves, foundations of quantum mechanics, measurement theory, coherence in electron scattering, microelectronics.

S. Frabboni, A. Gabrielli, G. C. Gazzadi, F. Giorgi, G. Matteucci, G. Pozzi, N. Semprini Cesari, M. Villa and A. Zoccoli — University of Modena and Reggio Emilia, CNR-Institute of Nanoscience-S3, University of Bologna and INFN Bologna. Ultramicroscopy 116 (2012) 73–76. Received 20 July 2011, accepted 23 March 2012.

(Abstract only — see the rights note above for why the full text is not reproduced here. The complete article, with the scanning-electron image of the milled slits, the stack of single-hit frames, the interarrival-time histogram and the accumulated interference scatter plot, is at the source.)

Companion sheet on this site: Gerhard Grössing and colleagues’ attempt to derive exactly this pattern from classical trajectories plus diffusion caused by zero-point fluctuations is at /library/stm-7071935008. This paper is the measurement such a model has to match.

The way in

https://doi.org/10.1016/j.ultramic.2012.03.017LICENCE. Published in Ultramicroscopy 116 (2012) 73 to 76; the article carries the line copyright 2012 Elsevier B.V., all rights reserved, and the Crossref record carries only the Elsevier text-and-data-mining user licence, which is not a Creative Commons licence. OpenAlex and Unpaywall label the green deposit at hdl.handle.net/11380/741983 as cc-by, but that IRIS Modena record holds the bibliographic entry alone — its own metadata marks the item as print and it carries no Creative Commons statement — so the label is a repository-level guess and is not honoured here. This sheet therefore holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims below are read against the complete four-page article, retrieved on 2026-09-08 from a publicly posted copy of the version of record, and the locators use the article’s own section, figure and page numbering. The authors are at the University of Modena and Reggio Emilia, CNR-Institute of Nanoscience-S3, the University of Bologna and INFN Bologna; Giulio Pozzi is the corresponding author. REGISTRY CORRECTION: the record reached the library with an eight-name author list that omitted Antonio Zoccoli, the ninth author on the paper’s own title page; the full list is restored here. The record also carried chapter ch10 alone; chapter 2 is added, because this is the bench any account of interference in terms of a real vacuum has to reproduce.

How to cite it

Stefano Frabboni, Alessandro Gabrielli, Gian Carlo Gazzadi, Filippo Giorgi, Giorgio Matteucci, Giulio Pozzi, Nicola Semprini Cesari, Mauro Villa, Antonio Zoccoli (2012) The Young-Feynman two-slits experiment with single electrons: Build-up of the interference pattern and arrival-time distribution using a fast-readout pixel detector. doi:10.1016/j.ultramic.2012.03.017

Where it sits in the curriculum

What the vacuum is Scalar waves and the field behind the fields