| Summary: | Periodically driven quantum systems, known as Floquet systems, have been a
focus of non-equilibrium physics in recent years, thanks to their rich
dynamics. Not only time-periodic systems exhibit symmetries similar to those in
spatially periodic systems, but they also display novel behavior due to
symmetry breaking. Characterizing such dynamical symmetries is crucial, but the
task is often challenging, due to limited driving strength and the lack of an
experimentally accessible characterization protocol. Here, we show how to
characterize dynamical symmetries including parity, rotation, and particle-hole
symmetry by observing the symmetry-induced selection rules between Floquet
states. Specifically, we exploit modulated quantum driving to reach the strong
light-matter coupling regime and we introduce a protocol to experimentally
extract the transition elements between Floquet states from the coherent
evolution of the system. Using the nitrogen-vacancy center in diamond as an
experimental testbed, we apply our methods to observe symmetry-protected dark
states and dark bands, and the coherent destruction of tunneling effect. Our
work shows how to exploit the quantum control toolkit to study dynamical
symmetries that can arise in topological phases of strongly-driven Floquet
systems.
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