Historical research guide · 0651 · 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
Stefano Frabboni · Alessandro Gabrielli · Gian Carlo Gazzadi · Filippo Giorgi · Giorgio Matteucci · Giulio Pozzi · Nicola Semprini Cesari · Mauro Villa · Antonio Zoccoli
In one minute
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.
Connection
Chapter 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.
From the source
The 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
The 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
The 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
The 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
The 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
What 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
The way in
https://doi.org/10.1016/j.ultramic.2012.03.017How 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