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We study the dissipative dynamics of a two-level system under ultrastrongdriving when the frequency and strength of the exciting field exceedsignificantly the transition frequency. We find three qualitatively differentregimes of such dynamics: 1) the collapse and revival of oscillations in thepopulation difference, 2) the simple exponential decay of the oscillationsresulting in their steady state with the finite amplitude, and 3) thesteady-state stabilization of the equally populated levels. The nonmonotonicBessel-function-like dependence on the driving strength is also predicted forthe decay rate of these oscillations. The features of this dependence aredetermined by the relative rates of energetic relaxation and pure dephasing.

Dissipative two-level systems under ultrastrong off-resonant driving