When nuclei catch up with electrons

Understanding the dynamics of quantum-mechanical systems on their natural time scale is the main goal in attosecond science. Among the most interesting systems to investigate are molecules, which have a very high degree of complexity, in particular when compared to atomic systems. So far, the few attosecond experiments performed on molecules have provided valuable insight into electron dynamics. In these studies, the dynamics of the nuclei around which the electrons evolve was assumed to be ‘frozen’, given that nuclei are much heavier than electrons and therefore move more slowly. However, even in the attosecond time regime, the approximation that electronic and nuclear motion are decoupled from one another is often not justified. In particular in molecules composed of light atomic species, the nuclear motion can be as fast as electron dynamics, resulting in a strong coupling between the two.

A team led by Dr. Laura Cattaneo and Prof. Ursula Keller at the Institute for Quantum Electronics of ETH Zurich has now studied the lightest and smallest of all molecules, H₂, and explored what happens when nuclear and electronic motion happen on a comparable time scale. As they report in an article published today in Nature Physics, they found that in molecules ionization delays — the time between the absorption of a photon and the emission of an electron during photoionization — can significantly depend on the kinetic energy of both the photoelectron and the nuclei. This finding extends the concept of ionization delays introduced for atomic systems. Variations of ionization delays with the nuclear kinetic energy can be as large as variations with the electronic kinetic energy. This implies that whenever light atoms are involved in the molecular ionization process, the outgoing electron wave packet cannot be disentangled from the nuclear wave packet.

These measurements at the attosecond time scale are based on an experimental approach developed earlier in the Keller group. In the so-called AttoCOLTRIMS apparatus (see the figure) attosecond metrology is combined with the imaging technique COLTRIMS, in which the correlated properties of the fragments of a molecular reaction can be recorded. This experimental capability was combined with nearly exact ab initio theory, performed by collaborators at the Universidad Autónoma de Madrid (Spain), to describe both electronic and nuclear motions, as well the coupling between them.

The significance of this work goes well beyond the simple H₂ molecule studied. Hydrogen atoms are present in most organic and biologically relevant molecules. Understanding the effects and contributions from coupled electron and nuclear dynamics present in such systems should therefore provide fundamental insight that will be important in various fields of research.