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MO: Fachverband Molekülphysik

MO 24: Attosecond Physics II (joint session A/MO)

MO 24.5: Vortrag

Donnerstag, 13. März 2025, 12:15–12:30, GrHS Mathe

A rigorous and universal approach for highly-oscillatory integrals in attosecond science — •Anne Weber¹, Job Feldbrugge², and Emilio Pisanty¹ — ¹Attosecond Quantum Physics Laboratory, King's College London, WC2R2LS London, UK — ²Higgs Centre for Theoretical Physics, University of Edinburgh, UK

Light-matter interactions within the strong-field regime, such as high-harmonic generation, typically give rise to highly-oscillatory integrals, which are often solved using saddle-point methods. Not only do these methods promise a much faster computation, but they also inform a more intuitive understanding of the process in terms of quantum orbits, as the saddle points correspond to interfering quantum trajectories (think Feynman's path integral formalism). Despite these advantages, a sound understanding of how to apply saddle-point methods to highly-oscillatory integrals in a rigorous way, and with algorithms which work uniformly for arbitrary configurations and laser drivers, remains lacking. This hinders our ability to keep up with state-of-the-art experimental setups which increasingly rely on tightly-controlled laser waveforms. Here, I will introduce the key ideas of Picard-Lefschetz theory -- the foundation of all saddle-point methods -- and their implementation. Using high-harmonic generation and above-threshold ionisation as examples, I will show how those ideas provide a robust framework for the fast computation of integrals, as well as a widely-applicable algorithm to derive the relevant semiclassical quantum orbits that underlie the physical processes.

Keywords: High-harmonic generation; two-colour fields; Picard-Lefschetz theory; saddle-point methods; strong-field physics