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Researchers use laser to ‘photograph’ the forbidden passage of electrons

In quantum mechanics, particles can travel through areas that are forbidden according to classical physics, a phenomenon called tunnelling. Researchers at Aarhus University and ETH Zurich in Switzerland have now mapped precisely where the particle emerges after its passage.

Figure 1: The principle of the attoclock technique. A powerful infrared laser pulse is directed through a quarter-wave plate to produce an almost circularly polarised light. The laser pulse is channelled through a supersonic gas cloud of helium or argon, ionising the atoms and thereby permitting the tunnelling. The circularly polarised light can be used as a kind of clock face, with the final direction and speed of the electron and the direction of the circularly polarised light at the time of ionisation functioning like the hands on a clock.
Figure 2: The red dots represent collected data of the electron’s angle of deflection (?) in connection with tunnelling in argon as a function of the laser strength. The greater the strength, the smaller the angle of deflection. The curves show the predictions of the angle of deflection according to different theories. The red line that appears to best match the data material is TIPIS (tunnel ionisation in parabolic coordinates with induced dipole and Stark shift) – the new theory developed by the Aarhus physicists. The name indicates that the theory was formulated using parabolic coordinates, taking shifts in both energy and multi-electron effects into account.
Associate Professor Lars Bojer Madsen, Department of Physics and Astronomy, Aarhus University.

In quantum mechanics, weird and wonderful things happen that go against common sense. A particle can, for example, break through a potential barrier even though the barrier’s energy is greater than the particle’s binding energy. This phenomenon is known as tunnelling. Figuratively speaking, this corresponds to a ball being capable of rolling over a hill without having sufficient speed to get to the top.

Three years ago, the Swiss professor Ursula Keller and her team at ETH Zurich (the Swiss Federal Institute of Technology) discovered that tunnelling takes no time at all.

Collaboration between Aarhus University and the university in Zurich has now succeeded in getting even closer to this mysterious phenomenon. The two teams of physicists have mapped with great precision exactly where the particle – in this case an electron – emerges after tunnelling.

This collaboration began when the team in Switzerland asked physicists in Aarhus for help to explain the theory behind their experimental results. The Aarhus physicists took up the challenge and found an answer.

“The Aarhus theory takes a number of effects into account that have previously been omitted in mapping the exit point. We use the right ‘natural coordinates’, include the change in energy from the state before tunnelling, and take the multi-electron effect into account, i.e. the effect of the other bound electrons,” says Associate Professor Lars Bojer Madsen, Department of Physics and Astronomy, Aarhus University.

He developed the theory together with Postdoctoral Scholar Darko Dimitrovski and Postdoctoral Scholar Mahmoud Abu-samha, also from the Department of Physics and Astronomy.

The theory provides the most precise predictions to date of the particle’s exit point and has just been published in Nature Physics along with the experimental results.

A still shot of the electron’s passage using ultrashort laser pulses

The Swiss team ‘photographed’ the electron’s passage through the potential barrier using strong ultrashort laser pulses. The pulses are like a fast flash that gives the researchers a sequence of images of the electron’s passage.

In the new experiments, the use of circularly polarised light for the laser pulses instead of linearly polarised light is particularly revolutionary. It means that the electric and magnetic fields that constitute the electromagnetic waves we know as light circulate around the beam’s direction of propagation (see figure 1).

“The use of circularly polarised light is unique because it constantly drives the electron away from the atom, enabling us to isolate and determine its exit point. When using linearly polarised light, the electric field pulls the electron back when the direction of polarisation changes, and the returning electrons thereby pollute the measurements,” Dr Dimitrovski explains.

New theory contributes to improving attoscience

This new method is called the attoclock technique and it belongs to a branch of physics known as attoscience. Attoscience breaks down the movement of electrons along their natural timescale and scale of longitude. The name is related to the atomic timescale – attoseconds (10-18 seconds). It thus takes the electron in a hydrogen atom around 20 attoseconds to complete a circle around the nucleus.

The Swiss group from ETH Zurich is a world leader in experimental attoscience, and the university is among the absolute best in the world – with thirty-one Nobel Prize winners, including Albert Einstein.

“There are very few top experimental groups in the world, and Ursula Keller’s group is one of them. They could pick and choose between the groups of theorists, but they chose us because of the expertise we’ve developed in recent years in describing processes in circular fields,” the associate professor says.

He predicts that the new results will have a huge impact on the attoscience of the future.

“We provide a much more detailed understanding of the steps in the tunnelling process, which is vital for the development of light pulses and measuring techniques at the attosecond level,” he says.

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Revised 15.03.2024