Ultrafast Control of Quantum Materials: Floquet Band Engineering and Beyond

A major goal of condensed matter physicists is to control the properties of materials. Permanent changes are made by shaping the material into nanoribbons or by embedding defects and impurities, for instance. Alternatively, temporary modifications to properties may be achieved by applying picosecond laser pulses. Such external time-periodic control, also known as Floquet engineering, significantly affects both the electronic energy band structures and the transport properties of quantum materials. In particular, I will discuss the Floquet graphene antidot lattice, a periodically hole-patterned graphene sheet subject to near-IR radiation. We demonstrate that the system can be steered through semiconducting, Dirac, selectively dynamically localized, and semi-Dirac Floquet electronic phases by simply tuning the intensity of the incident radiation. On the basis of a generalized linear response theory, we also compute its optical conductivity signatures, which is an important stepping stone for comparing with contrast reflectance experiments. I will conclude by discussing the issue of high-fidelity Floquet state preparation by framing the determination of the laser amplitude modulation as an inverse problem through the lens of quantum optimal control