Quantum Electronics: Tunneling Effect In Strong Laser Field Interaction Under Attack

When new technologies allow theoretical models to be tested experimentally, scientists must be prepared to say goodbye to accepted thought patterns. The current publication by Professor Ursula Keller and her team at the Institute of Quantum Electronics of ETH Zurich could bring about just such a break with accepted wisdom. The group succeeded for the first time ever in measuring experimentally the tunnelling delay times of electrons ionized in strong laser fields.

The tunnelling effect is responsible for the ability of bound electrons in atoms to pass through an energy barrier even though the barrier’s energy is higher than the electron’s binding energy. According to classical physics, overcoming this barrier is impossible, hence the assumption of a quantum-mechanical process.

A popular way of illustrating this is to imagine a ball that does not have enough momentum to surmount a hump, so simply “tunnels through” it instead. Keller says “Contrary to some accepted theories, our measurement has shown that this so-called tunnelling ionisation takes place with almost no delay. The results of her most recent experiments appear in a recent issue of the scientific journal “Science”.

Calibration problems solved

Based on calculations by several theoreticians, it was assumed that an electron took between 500 and 600 attoseconds (10-18 sec.) to tunnel through a laser-induced tunnelling barrier. A time interval of this kind was not measurable until recently, even using the shortest laser pulses. However, Keller’s team presented a method in “Nature Physics” last June that enables measurements down to 25 attoseconds by using femtosecond laser pulses (see the box and the ETH Life article A stopwatch for the tunnel effect). Keller’s results at that time gave hope that the tunnelling time would soon be measured. However, calibration problems still stood in the way of this enterprise.

To make a measurement in the region of a few attoseconds it is essential to calibrate “time zero”, i.e. the absolute zero point of the time measurement. In the end the calibration was easier than had been assumed last summer: if the original direction of the laser field used for the measurement is determined unequivocally, a clear reference point is obtained for the angle of the laser clock’s “hour hand”. Keller says, not without pride, “We now have a clock with an average accuracy of six attoseconds, or twelve if the error tolerance is included. This is, without doubt, the most precise clock in the world.”

No tunnelling time in the classical sense

The team now set about using this instrument to check the tunnelling time in the laser-induced ionisation of helium atoms. Keller explains that “There are many theories about the tunnelling process, but the authors often use the expression “tunnelling time” to describe completely different things.” Her group agreed on the term “tunnelling delay time”, and, in their current publication, they refer to the tunnelling time according to Keldysh and the “Büttiker-Landauer traversal time for tunnelling”.

Physicists have hitherto assumed that the delay resulting from “tunnelling through” the energy barrier is measurable by using an attosecond clock. However, Keller’s group were unable to demonstrate any such “tunnelling time” in the experiment (with an upper limit of 12 attoseconds averaged over different laser field strengths and limited by the measurement accuracy). The measurement was recalculated by the quantum theorist Harm Geert Muller. He concluded that the results are in agreement with numerically solving the time-dependent Schrödinger equation, one of the fundamental laws of quantum mechanics. Nevertheless, Keller does not claim that the tunnelling times according to Keldysh are wrong, “but they do not describe a “real” tunnelling time according to our classical understanding, rather something different.” The same is also true for the “Büttiker-Landauer traversal time for tunnelling”, which is entirely self-consistent, as Markus Büttiker from the University of Geneva, one of the authors of this theory and a co-author of the current Science publication, was able to explain to the ETH Zurich group.

Room for new ideas and theories

Physicists – including Ursula Keller – are greatly astonished that the concept of “tunnelling through” in the laser-induced ionisation of atoms, which was accepted for many years, may now prove to be inadmissible. The physicist warns that, “Science benefits from such easily understandable pictures to reduce complexity, but they often have a limited scope of application and may even lead people astray and towards wrong ideas.”

For Ursula Keller, such breaks with accepted ideas are precisely what makes quantum physics so fascinating. Keller hopes that, “Perhaps our results will provoke a whole series of quantum physicists to re-think their theories, thus making room for new ideas.” She has been visiting universities for several weeks and has discussed her results with physicists at Columbia University in New York, Stanford in California, Southampton and Berlin. The physicist calls this “hawking” and uses it to underline her claim not only to publish scientific results but also to take an active part in their discussion throughout the world.

The attosecond clock

The “attoclock” attosecond clock, which occupies the space of two laboratories, is based on an almost circularly polarised infrared laser pulse and a “COLTRIMS” (Cold Target Recoil Ion Momentum Spectroscopy) detector. In this device, the laser pulses move in a circle in space rather than in the form of a wave as is normally the case with a light beam. The electrical field of the infrared light rotates once through 360° in space over 2.4 femtoseconds (fs). This creates a kind of clock face with an attosecond pointer instead of a second hand. The length of the infrared pulse is only about 5 fs, which means that the laser-induced tunnelling ionisation takes place in principle within one revolution of the pointer. Proof of the functioning of the clock with a helium atom was first published in July 2008. The “attoclock” was used to make the most precise measurements of time carried out so far in the atomic physics of strong fields.