29 July 2025 Tue 4 pm

Periodically driven (Floquet) systems offer a powerful and versatile framework for simulating complex quantum phenomena, leveraging time-periodic modulation — known as Floquet engineering — as a dynamic resource. This colloquium explores the rich theoretical landscape and practical implications of Floquet theory in the context of quantum simulation. Beginning with the fundamentals of Floquet formalism, we discuss how periodic driving can effectively realize static Hamiltonians with engineered properties, enabling access to novel phases of matter and synthetic gauge fields. We address key challenges such as heating, energy absorption, and the dynamics of thermalization, highlighting mechanisms of prethermalization that can stabilize useful non-equilibrium states. The interplay between adiabaticity and driving is examined through the lens of the quantum adiabatic theorem and counterdiabatic driving techniques. In particular, we show how to reformulate Floquet theory as a shortcut to adiabaticity by deriving the former from the adiabatic theorem. Finally, we present geometric Floquet theory and advanced Floquet control schemes that further broaden the toolbox for precise manipulation of quantum systems, facilitating fast and controlled quantum state preparation in the presence of strong periodic drives. The colloquium aims to present a coherent narrative connecting foundational concepts to cutting-edge developments, emphasizing the utility of periodic driving as a cornerstone for next-generation quantum technologies.

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