Martin Thümmler

High-order harmonic generation (HHG) in solids offers a promising route to compact ultrafast sources of quantum light, but its efficiency and coherence are limited by ultrafast dephasing of laser-driven electron–hole polarization. Although widely described by a phenomenological coherence time, the microscopic origin of this dephasing has remained unresolved. Here, we combine wavelength-dependent HHG measurements in monolayer and bulk semiconductors with ab initio many-body calculations of electron–phonon scattering and strong-field simulations. We show that the measured wavelength scaling of the HHG yield is quantitatively reproduced only when semiconductor Bloch equations incorporate momentum-dependent dephasing derived from first principles scattering rates. The calculations reveal that strong-field-driven carriers rapidly enter regions of the Brillouin zone with enhanced electron–phonon scattering, giving rise to effective few-femtosecond dephasing. Our results establish a microscopic foundation for dephasing in solid-state HHG and provide a framework for engineering coherence in strongly driven solids for quantum photonic applications.

The Berry connection is a gauge-dependent quantity frequently used to describe the optical response of solids. Its evaluation requires a k derivative with respect to the cell-periodic part of the Bloch functions and is commonly calculated in the Wannier basis by using overlap matrices of cell-periodic parts of Bloch functions at neighboring k points. So far, all proposed interpolation schemes for the Berry connection do not account for the matrix structure of the overlap matrices explicitly but treat the matrix elements as independent, or only distinguish between diagonal and off-diagonal entries. In this work, we propose a self-consistent interpolation scheme based on the matrix logarithm resulting in a strongly improved accuracy. Furthermore, we discuss how the basis set incompleteness of the bands used in the calculation imposes constraints on the accuracy. We quantify the basis incompleteness based on the singular values of the overlap matrices and relate it to the invariant part of the spread functional Ω I of the Wannier functions. Numerical calculations for monolayer MoS 2 and bulk Si demonstrate that the proposed interpolation scheme is much less sensitive to the Wannierization details and leads to an improved quality of the velocity matrix and the optical conductivity.

Recently, the size-dependence of high-order harmonic generation (HHG) in quantum dots (QDs) has been investigated experimentally. In particular, for longer driving wavelengths and quantum dots smaller than 3 nm, HHG was strongly suppressed; however, there is no computational model capable of describing the strong-field response of such systems. In this work, we introduce a computationally efficient three-dimensional real-space tight-binding model specifically designed for the simulation of HHG in confined systems. The model parameters are meticulously derived from density functional theory calculations for the semiconductor bulk, followed by a process of Wannierization. Our findings demonstrate that the proposed model accurately captures the observed dependency of the HHG yield on the quantum dot size. In addition, we simulate the HHG yield for elliptically polarized pulses for different QD-sizes and driving wavelengths up to 5 μm. The proposed model fills the theoretical void in simulating HHG within medium-sized nanostructures, which cannot be described by methods applied for periodic solids, or small molecules or atoms.

We report here on results of systematic experimental-theoretical investigation of high-order harmonic generation (HHG) in layers of CdSe semiconductor quantum dots of different sizes and a reference bulk CdSe thin film. We observe a strong decrease in the efficiency, up to complete suppression of HHG with energies of quanta above the band gap for the smallest dots, whereas the intensity of below band gap harmonics remains weakly affected by the dot size. In addition, it is observed that the suppression of the above gap harmonics is enhanced with increasing the driving wavelength. These systematic investigations allow us to develop a simple physical picture explaining the observed suppression of the highest harmonics: the discretization of electronic energy levels seems to be not the predominant contribution to the observed suppression but rather the confined dot size itself, causing field-driven electrons to scatter off the dot's walls. The reduction in the dot size below the classical electron oscillatory radius and the corresponding scattering limits the maximum acceleration by the laser field. Moreover, this scattering leads to a chaotization of motion, causing dephasing and a loss of coherence, therefore suppressing the efficiency of the emission of highest-order harmonics. Our results demonstrate a regime of intense laser-nanoscale solid interaction, intermediate between the bulk and single-molecule response, and are crucial for nanophotonic platforms aiming at control over high-order harmonic properties and efficiency.