M.Sc Thesis

M.Sc StudentEven Tzur Matan
SubjectDynamical Symmetry Breaking in High
Harmonic Generation
DepartmentDepartment of Physics
Supervisor PROF. Oren Cohen
Full Thesis textFull thesis text - English Version


Floquet systems often exhibit dynamical symmetries (DS) that govern the time-dependent dynamics and result in selection rules. When a DS is broken by a perturbation, deviations from the selection rules of the symmetric system are expected. While these deviations are often used for exploring the perturbations and perturbed dynamics, so far, they are not described by a general theory.  In this thesis, I consider dynamical symmetry breaking in Floquet systems from a general standpoint, using a symmetry breaking laser field as a model perturbation.

In the first section of this thesis, I utilize Floquet perturbation theory to formulate and tabulate ‘selection rules’ for the allowed contributions to selection rule deviations induced by such a field. I find that this approach results in universal scaling laws for selection rule deviations in high harmonic generation and Floquet systems in general. The robustness of the derived scaling laws is illustrated through numerical calculations of the scaling of the HHG spectrum with such a perturbation.

Then, in the second section of this thesis, I identify that the selection rules we derived by the perturbative approach are a manifestation of an unexplored class of DS in what at first glance appear to be symmetry broken systems but are in fact systems that exhibit synthetic dynamical symmetries (SDSs).  That is, dynamical symmetries in a high dimensional synthetic space. We formally tabulate such SDS in (2)D Floquet systems dressed by an external monochromatic laser field, as well as derive their corresponding selection rules for HHG. Elegantly, these selection rules not only reproduce the selection rules we have derived in the previous section, but also impose additional constraints on the polynomial expansion of the emission, to all orders in perturbation strength.

Lastly, I compare the predictions of the theoretical approaches developed in this thesis to experimental data of DS breaking in HHG. Notably, the theory describes the results of the experiment with high precision.

Overall, the analytical theory’s predictions are robust, and provide a universal framework for analyzing various, up to now unconnected, symmetry breaking perturbations. For instance, we have shown explicitly that the theory is useful for analyzing symmetry-breaking due to imperfect polarization components in the driving laser, but it can similarly (and easily) be applied to other types of symmetry breaking due to intrinsic properties of the medium, or properties of the light-matter dressed system.