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  • Electron-Guiding Mimics Optical Fiber Waveguides
May 2011
GARCHING, Germany, May 12, 2011 — A new technique that resembles the guiding of light waves in optical fibers has been used to efficiently guide slow electrons purely by electric fields for the first time. The achievement involves guiding the electrons by applying a microwave voltage to electrodes fabricated on a planar substrate and is promising for a variety of applications, from guided matter-wave experiments to noninvasive electron microscopy.

The investigation of the properties of electrons plays a key role in the understanding of the fundamental laws of nature. Electrons were the first elementary particles to reveal their wavelike properties and have been important in the development of quantum mechanics theory. However, being extremely small and quick, electrons are difficult to control.

Figure 1. Photograph of the guide with the electron source in the back. The white lines are the substrate that is visible in the space between the individual electrodes. Electrons are emitted through a tiny 20-µm-diameter hole (not visible) in the center of the gun. The guiding minimum forms 0.5 mm above the electrodes. Guided electrons follow the direction of the electrodes and turn to the left in the foreground of the picture.

Measurements involving confined electrons have so far been performed mainly in so-called Penning traps, which combine a static magnetic field with an oscillating electric field. The new work was conducted by a team led by Peter Hommelhoff, head of the Ultrafast Quantum Optics research group at the Max Planck Institute of Quantum Optics, and their findings are described in the May 9 advance online edition of Physical Review Letters.

For a number of experiments with propagating electrons, such as interferometry with slow electrons, it would be advantageous to confine the electrons by a purely electric field. This can be done in an alternating quadrupole potential similar to the standard technique that is used for ion trapping. These so-called Paul traps are based on four electrodes to which a radio-frequency voltage is applied. The resulting field evokes a driving force that keeps the particle in the center of the trap. In 1989, Wolfgang Paul received the Nobel Prize in physics for inventing these traps.

For several years now, scientists have realized Paul traps with microstructured electrodes on planar substrates, using standard microelectronic chip technology. For the first time, Hommelhoff and his group have applied this method to electrons.

Since the mass of these pointlike particles is only one-tenth of a thousandth of the mass of an ion, electrons react much faster to electric fields than to the rather heavy ions. Hence, to guide electrons, the frequency of the alternating voltage applied to the electrodes has to be much higher than for the confinement of ions and is in the microwave range, at around 1 GHz.

In the experiment, electrons are generated in a thermal source (in which a tungsten wire is heated, such as in a lightbulb), and the emitted electrons are collimated to a parallel beam of a few electron volts. From there, the electrons are injected into the waveguide. It is being generated by five electrodes on a planar substrate to which an alternating voltage with a frequency of about 1 GHz is applied (see Figure 1 above).

Figure 2. Overview of the experimental setup and signals of guided and unguided electrons. (a) Picture of the setup as seen from above with the substrate in the center. The last element of the electron gun is visible in the top left corner. Guided electrons follow the curved orange path from the source to the detector, whereas unguided electrons travel in straight lines over the substrate (indicated in blue). (b) Guided electrons result in a bright spot at the exit of the guide (indicated by an orange circle). (c) With no guiding voltage applied, the electrons hit the detector on the right side, where a diffuse spot is forming.

This introduces an oscillating quadrupole field in a distance of half a millimeter above the electrodes, which confines the electrons in the radial direction. In the longitudinal direction, there is no force acting on the particles, so they are free to travel along the "guide tube." As the confinement in the radial direction is very strong, the electrons are forced to follow even small directional changes of the electrodes.

To make this effect more visible, the 3-mm-long electrodes are bent to a curve of 30° opening angle and with a bending radius of 40 mm. At the end of the structure, the guided electrons are ejected and registered by a detector. As shown in Figure 2b, a bright spot caused by guided electrons appears on the detector right at the exit of the guide tube, which is situated in the left part of the picture. When the alternating field is switched off, a more diffusively illuminated area shows up on the right side (Figure 2c). It is caused by electrons spreading out from the source and propagating on straight trajectories over the substrate.

"With this fundamental experiment, we were able to show that electrons can be efficiently guided by purely electric fields," said Hommelhoff. "However, as our electron source yields a rather poorly collimated electron beam, we still lose many electrons."

In the future, the researchers plan to combine the new microwave guide with an electron source based on field emission from an atomically sharp metal tip. These devices deliver electron beams with such a strong collimation that their transverse component is limited only by the Heisenberg uncertainty principle.

Under these conditions, it should be feasible to investigate the individual quantum mechanical oscillations of the electrons in the radial potential of the guide.

"The strong confinement of electrons observed in our experiment means that a 'jump' from one quantum state to the neighboring higher state requires a lot of energy and is therefore not very likely to happen," said Johannes Hoffrogge, a doctoral student on the team.

"Once a single quantum state is populated, it will remain so for an extended period of time and can be used for quantum experiments." This would make it possible to conduct quantum physics experiments such as interferometry with guided slow electrons. Here the wave function of an electron is first split up; later on, its two components are brought together again, whereby characteristic superpositions of quantum states of the electron can be generated. But the new method could also be applied for a new form of electron microscopy.

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The study and utilization of interference phenomena, based on the wave properties of light.
quantum mechanics
The science of all complex elements of atomic and molecular spectra, and the interaction of radiation and matter.
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