  Spatial symmetries of quantum systems leads to important effects in
spectroscopy, such as selection rules and dark states. Motivated by the
increasing strength of light-matter interaction achieved in recent experiments,
we investigate a set of dynamically-generalized symmetries for quantum systems,
which are subject to a strong periodic driving. Based on Floquet response
theory, we study rotational, particle-hole, chiral and time-reversal symmetries
and their signatures in spectroscopy, including symmetry-protected dark states
(spDS), a Floquet band selection rule (FBSR), and symmetry-induced transparency
(siT). Specifically, a dynamical rotational symmetry establishes dark state
conditions, as well as selection rules for inelastic light scattering
processes; a particle-hole symmetry introduces dark states for symmetry related
Floquet states and also a transparency effect at quasienergy crossings; chiral
symmetry and time-reversal symmetry alone do not imply dark state conditions,
but can be combined to the particle-hole symmetry. Our predictions reveal new
physical phenomena when a quantum system reaches the strong light-matter
coupling regime, important for superconducting qubits, atoms and molecules in
optical or plasmonic field cavities, and optomechanical systems.
