Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms
By Darko Dimitrovski and Lars Bojer Madsen
New theory and experiments emerging from collaboration between ETH, Zurich, Switzerland, and the Department of Physics and Astronomy, Aarhus University, Denmark, show that it takes no time for an electron to tunnel through a classically forbidden area, and that it is possible to map out the point in space at which the electron escapes the tunnel with sub-angstrom precision – two important contributions to the emerging field of attoscience.
Just as in photography, where a fast flash can capture an instantaneous image of a moving object, a sufficiently short laser pulse can be used to probe matter at a microscopic level. The natural timescale for the motion of electrons around atomic nuclei is the attosecond (10-18 seconds), and new light sources with ultra-short duration and/or high intensity, combined with new measurement techniques, are currently providing experimental access to this regime. The capabilities of attosecond and strong femtosecond laser pulses open up new avenues for time-dependent studies of multi-electron dynamics in atoms, molecules, plasmas and solids on their natural timescale – the attosecond. In addition, the spatial resolution achieved is smaller than the dimensions of molecules and atoms. These capabilities promise an increase in our knowledge and understanding of matter on a microscopic level.
One of the processes that can be imaged on the attosecond timescale is tunnelling. Tunnelling itself is one of the most striking manifestations of quantum mechanics as it describes the possibility for a particle to move through a potential barrier that is higher than the energy of the particle. On the other hand, the tunnelling of an electron through the barrier formed by the electric field of the laser and the atomic potential is the initial key process that triggers dynamics in strong-field science and attoscience. A detailed understanding of the tunnelling step is therefore of paramount importance for attoscience, including the generation of attosecond pulses and attosecond measurement techniques.
In a recent work published in Nature Physics, the experimental group of Ursula Keller, ETH, Zurich, and theoreticians Darko Dimitrovski, Mahmoud Abu-samha and Lars Bojer Madsen, Department of Physics and Astronomy, Aarhus University, elucidated the fundamental process of tunnelling ionisation in atoms with unprecedented accuracy. Using the so-called attoclock technique – an ultrafast technique used to study the timing of processes in matter on the attosecond timescale – a momentum distribution of liberated electrons was measured. The influence of the ionic potential and the tunnel exit point is encoded in the overall shift of the momentum distributions – the offset angle. With the help of the theory developed in Aarhus, it was shown that the experimentally monitored quantity (the offset angle) directly addresses the tunnel exit point as a function of field strength, without having to determine the tunnel rate exactly. In that sense, the combined experiment and theory work provide a unique study of the electron-parent ion interaction with unprecedented precision in time and space.
The new theory accounts for the shift of the energy of the initial bound state in the field and it includes for the first time a multi-electron effect describing how the polarization by the laser of the remaining electrons affects the dynamics of the tunnelling electron, and the theory assumes zero tunnelling time.
The main findings of the study are that the theory enables the determination of the flow of the tunnelling current, answering where the electron goes after ionisation. Due to the negative charge of the electron, the intuitive answer to the latter would be in the direction opposite to the instantaneous field. This is true for larger distances from the atomic centre. Yet, even in textbooks, the separation of the physical problem of an electron in the combined potentials of an external field – a pure Coulomb field – is accomplished in the so-called parabolic coordinates, reducing the 3D problem into 1D and enabling an analytic description: the tunnelling current is permitted to flow along only one of the parabolic coordinates. The comparison between theory and experiment shows that this particular geometry of the tunnelling current flow holds for real atoms where the potential deviates from the Coulomb one and where multi-electron effects might be important. These results have implications for the laser-induced tunnelling of atoms and molecules and for the analysis of time-resolved measurements on the attosecond timescale.
Contact
Darko Dimitrovski
Department of Physics and Astronomy
Aarhus University
+45 8942 3668
darkod@phys.au.dk
Lars Bojer Madsen
Department of Physics and Astronomy
Aarhus University
+45 8942 3674
Mobile +45 2338 2392
bojer@phys.au.dk
- Attoclock set-up. An intense infrared laser pulse is propagated through a quarter-wave plate to produce a close-to-circularly polarised laser field. This pulse is then focused into a supersonic gas target to tunnel-ionise helium or argon. The ions and electrons are guided onto time and position-sensitive detectors to determine, in coincidence, the momenta of the atomic fragments after the laser pulse.
- Ion momentum distribution and the angular offset θ. The dashed line is the maximum of the distribution, which is shifted to the minor polarisation axis (full line).
- Offset angle for Ar. Experimental data for θ obtained from electron momentum distributions in argon as a function of laser intensity, together with the curves predicted by different models (red dots with error bars). The full red curve denoted as TIPIS is the new theoretical model developed in Aarhus.
