Counterdiabatic Driving for Periodically Driven Systems

Periodically driven systems have emerged as a useful technique to engineer the properties of quantum systems, and are in the process of being developed into a standard toolbox for quantum simulation. An outstanding challenge that leaves this toolbox incomplete is the manipulation of the states dressed by strong periodic drives. The state-of-the-art in Floquet control is the adiabatic change of parameters. Yet, this requires long protocols conflicting with the limited coherence times in experiments. To achieve fast control of nonequilibrium quantum matter, we generalize the notion of variational counterdiabatic driving away from equilibrium focusing on Floquet systems. We propose two approaches to find local approximations to the adiabatic gauge potential for the effective Floquet Hamiltonian, based on the inverse-frequency expansion and a non-perturbative variational principle. They enable transitionless driving of Floquet eigenstates far away from the adiabatic regime. We discuss applications to two-level, Floquet band, and interacting periodically-driven models. In particular, we demonstrate that the developed methods allow us to capture non-perturbative photon resonances and obtain high-fidelity protocols that respect experimental limitations like the locality of the accessible control terms. Our work lays the foundations for a quantum control theory of nonequilibrium systems.