Ultrafast dynamics and high-harmonic generation

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When irradiating a solid with ultra-short laser pulses (duration ~ 100 fs), electrons are excited from valence bands to conduction bands. The electric field of the laser pulse

???????????????? E(t) = E₀ cos?(ωt) exp?(?t?/σ?)

features a Gaussian envelope and is typically modulated with an oscillating frequency? ω in the Terahertz range [1]. From a driven harmonic oscillator, we expect the charge density to also oscillate with a frequency ω as response to the electric field. However, the electron dynamics in the material is complex: There are multiple excitation of electrons between bands and already excited electrons are accelerated by the electric field E(t). As a consequence, the electron charge density oscillates not only with frequency ω, but also with higher frequencies nω, n∈N. The emitted radiation by the charge density movement thus features high-harmonic frequencies nω, where n>20 can be observed.

In the project "Effects of interactions on high harmonic generation in topological insulators", we propose to extend our semiconductor Bloch equations code (https://github.com/ccmt-regensburg/CUED, [2]) to capture Coulomb interactions of the involved charge carriers. Once having the coding part finalized, we propose to investigate the effects of Coulomb interactions on the high-harmonic spectrum using the developed code. This project is suitable for a Bachelor or Master thesis.
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[1] C. P. Schmid, L. Weigl, P. Gr?ssing, V. Junk, C. Gorini, S. Schlauderer, S. Ito, M. Meierhofer, N. Hofmann, D. Afanasiev, J. Crewse, K. Kokh, O. Tereshchenko, J. Güdde, F. Evers, J. Wilhelm, K. Richter, U. H?fer, and R. Huber, Tunable non-integer high-harmonic generation in a topological insulator, Nature 593, 385-390 (2021)

[2] J. Wilhelm, P. Gr?ssing, A. Seith, J. Crewse, M. Nitsch, L. Weigl, C. Schmid and F. Evers, Semiconductor Bloch-equations formalism: Derivation and application to high-harmonic generation from Dirac fermions, Phys. Rev. B 103, 125419 (2021)