24 May 2017 To be or not to be localized?

Schematic Illustration of high harmonic generation in solids

A study published in PRX develops a mathematical model for high harmonic generation in solids. Generating high-order harmonics as a response of the laser-matter interactions have become a unique tool to explore the nature of the ultrafast electron dynamics in gases. This“high harmonic generation”or HHG, is important for creating pulses of light that last for just a billionth of a billionth of a second (an attosecond). So far, those attosecond light sources allow physicists to record the sub-femtosecond electronic transitions in gases. But what about the electron dynamics in solids and the HHG study?

A key feature of HHG in a gas is that ionized electrons recombine with their parent atoms; in a solid, the electron can recombine with any other atom in the crystal lattice. This “delocalization” is poorly understood, yet believed to be important for attosecond pulse generation and real-time imaging of the electronic wave function in the solid state or the electron density.

In the recent paper published in Physical Review X, researcher Edyta Osika from University of Science and Technology of Kravow-Poland, in collaboration with ICFO researchers Dr. Alexis Chacon and ICREA Prof at ICFO Maciej Lewenstein, as well as scientists from other research centers, including collaborator Dr. Marcelo F. Ciappina from ELI-Beamlines, Czech Republic, developed a mathematical model that addresses the fundamental question of how this delocalization contributes to HHG emission in a solid.

The analytic approach builds on a three-step model that is well known for accurately describing the harmonic emission phenomenon in a dilute gas. By using localized atomic sites in the valence band and a delocalized description in the conduction band, one can separate the contributions of neighboring lattice sites to each harmonic and hence determine delocalization in harmonic emission. These neighboring contributions vary significantly with harmonic frequency and band structure of a crystal. Interestingly, for crystals with narrower bands, the light emission shows significant localization, similar to what happens in a gas.

These results pave the way for controlling localized contributions to harmonic emissions in a solid crystal, with important implications for the emerging field of atto-nanoscience, which explores physics on very small scales with unprecedented time resolution. The‘existential’question of an electron in a solid, ‘to be or not to be localized’, could be, in principle, answered using this model and studying the features of the emitted harmonic radiation at different driven laser configurations.