Tunneling is a peculiar quantum phenomenon with no classical counterpart. It plays an essential role for strong field phenomena in atoms and molecules interacting with intense lasers. Processes such as high-order harmonic generation are driven by electron dynamics following tunnel ionization.

While this has been widely explored, the behavior of electrons under the tunneling barrier, though equally significant, has remained obscure. The understanding of laser-induced strong field ionization distinguishes two scenarios for a given system and laser frequency: the multiphoton regime at rather low intensities and tunneling at high intensities.

However, most strong-field experiments have been carried out in an intermediate situation where multiphoton signatures are observed while tunneling is still the dominant process.

A recent one-dimensional model by Michael Klaiber and Karen Hatsagortsyan from the theory division of Christoph Keitel at the Max-Planck-Institut für Kernphysik (MPIK) in Heidelberg predicted a new excitation mechanism: The electron may be reflected at the end of the tunnel—also a pure quantum effect. The paper is published in the journal Physical Review Letters.

While propagating backwards under the barrier, it gains additional energy sufficient to reach an excited state of the atom. This can then be subsequently ionized by absorption of a few photons. The current work applied this model to the strong-field ionization of xenon atoms, including both direct multiphoton ionization as well as under-the-barrier recollision in a full three-dimensional calculation.

A similar behavior was found for krypton atoms experimentally as well as theoretically, proving the more general relevance of under-barrier dynamics in strong laser fields. “The new findings expand our insights into the control of tunneling dynamics in laser spectroscopy and attosecond physics,” states Klaiber, theory author of the paper.

Moreover, the under-barrier resonances are also likely to induce similar substantial amendments and attosecond tunneling time delays in comparable scenarios, modifying, e.g., strong-field molecular, solid-state, and even high-energy tunneling quantum dynamics.