  We consider multiphoton dynamics of a quantum system composed of a
three-state atom (a qutrit) and a single-mode photonic field in the ultrastrong
and deep strong coupling regimes, when the coupling strength is comparable to
or larger than the oscillator energy scale. We assume a qutrit to be in a
polar-$\Lambda $ configuration in which two lower levels have mean dipole
moments. Direct multiphoton resonant transitions revealing generalized Rabi
oscillations, collapse, and revivals in atomic excitation probabilities for the
ultrastrong couplings are studied. In the deep strong coupling regime
particular emphasis is placed on the ground state of considering system which
exhibits strictly nonclassical properties.
