Quantum entanglement in HHG and topological light probes for chirality in strong-field physics

I will discuss our advancements along two main research directions. First, I will present a truly quantum optical theory of high-harmonic generation (HHG); this is the first approach that utilizes purely quantum simulations for both light and matter. In particular, we avoid using averaging procedures over 'semi-classical trajectories' for sampling quantum distribution functions of the electromagnetic field; rather, we solve the full time-dependent problem in a multi-dimensional manner on a real-space grid representation. This permits formulating entanglement measures by directly evaluating the photonic wave-functions. We show the first agreement with recent experiments, and predict various interesting properties of entanglement in HHG: (i) That it strongly depends on focal averaging, (ii) that it depends on long-range interactions in the system, (iii) that it can be manipulated by tuning the field power, and (iv) that entanglement should also exist between higher-order harmonic modes. Second, I'll present our recent results deriving a group theory for photoelectron chiral dichroism (PECD) from tailored light, predicting novel geometries for chiral discrimination, and yielding fundamental insights into the nature of PECD. I will show that PECD is also attainable if non-helical light fields are employed, leading to new PECD mechanisms relying on a generation of chiral hole wave packets instead of the traditional helical ionization process.