A unified time and frequency image to explain ultrafast atomic excitation in strong laser fields

The fact that light has to be understood either as an electromagnetic wave or as a stream of "energy quanta" (photons) pervades the history of quantum physics like a red thread. In the case of the interaction of intense short-pulse laser radiation, this dualism finds its equivalent in the vivid images used to describe ionization and excitation of atoms: the multiphoton image and the tunnel image. In a combined theoretical and experimental study of the ultrafast excitation of atoms in intense laser fields, researchers from the Max Born Institute succeeded in attributing and pointing out the two predominant and seemingly opposite explanations for the interaction of matter with intense laser radiation on an underlying nonlinear process. how both images can be transformed into each other. The study has appeared in the journal Physical Review Letters and has been awarded Editors' Suggestion by editors for their importance, innovation and broad impact. In addition to its basic message and meaning, the work reveals improved and new ways of accurately determining the laser intensity and the laser intensity-dependent control of the coherent state occupation of atomic levels.

Although with the Keldysh parameter, which was already introduced in the 1960s by the eponymous Russian physicist, a clear distinction was made between the multiphoton and tunnel image, it remains an open question whether, especially in the description of the excitation of atoms by intense laser fields that can be transformed into each other's two seemingly incompatible approaches.

The multiphoton character manifests itself e.g. in the presence of resonant increases in the excitation as soon as an integer multiple of the photon energy corresponds to the excitation energy of atomic states. However, one has to keep in mind that the atomic levels shift to higher energies with increasing laser intensity. As a result, resonant effects due to an increase in laser intensity occur even when the frequency of the laser radiation is fixed. These occur periodically, whenever the energy shift of the levels has increased by one photon energy. These areas are referred to as channel closing (completion of a multiphoton process with a fixed number of photons), since simultaneously with the increased excitation the ionization is suppressed.

In the tunnel image, the laser field is considered as an electromagnetic wave, of which only the oscillating electric field is considered. Excitation can be understood as a process in which the bound electron is initially released instantaneously through a tunneling process near the maximum of a field cycle. However, in many cases the electron does not absorb enough drift energy from the oscillation in the laser field in order to free itself from the Coulomb field of its fuselage at the end of the laser pulse, which would lead to the ionization of the atom. Instead, it finds itself in an excited Rydberg state again. In the tunnel image, no resonant effects in the excitation are possible because the laser field is assumed to be static for the tunneling process and thus the frequency of the light is initially insignificant.

Fig. 1: Yield of excited atoms as a function of the laser intensity. At a laser intensity of 200 TW / cm2, close to the channel closure for 6 photons, a strong resonant increase in excitation is shown by a factor of 100. For the argon data, the theoretical prediction is shown (red dashed curve) excellent agreement with the experimental data.

In the study, the yield of excited argon and neon atoms as a function of laser intensity was measured directly for the first time in both the multiphoton and tunnel regions. In the multiphoton region, pronounced resonant increases in the excitation probability were detected, in particular in the vicinity of the regular channel closings, while in the tunnel region the excitation probability no longer shows resonant structures. However, excitation could be observed even at high laser intensities beyond the intensity threshold for complete ionization.

The numerical solution of the time-dependent Schrödinger equation for the description of the investigated atoms in the strong laser field led to an excellent agreement of the theory with the experimental data in both areas. A closer analysis of the results shows that one can view the two images as a complementary description in frequency and time of one and the same nonlinear process. In the time frame, one can assume that periodic electron wave packets are generated in the maxima of the field cycles. In the multiphoton range, it can be seen that these wave packets are mainly generated in the laser pulse maximum and only interfere constructively when the intensity is close to the channel closings. Thus, regular increases in the excitation probability each result in the distance of the photon energy. Although in the tunnel region the wave packets are also generated periodically at the maxima of the field cycles, but mainly in the rising part of the laser pulse, so that they irregularly interfere, which leads to an irregular behavior in the excitation probability. These less pronounced rapid changes are not resolved in the experiment and therefore a smooth excitation spectrum is detected.

Original publication

Unified time and frequency picture of ultrafast atomic excitation in strong laser fields

H. Zimmermann, S. Patchkovskii, M. Ivanov, U. Eichmann

Physical Review Letters 118 (2017) 013003/1-5