Solvable model of dissipative dynamics in the deep strong coupling regime

We describe the dynamics of a qubit interacting with a bosonic mode coupled to a zero-temperature bath in the deep strong coupling (DSC) regime. We provide an analytical solution for this open system dynamics in the off-resonance case of the qubit-mode interac- tion. Collapses and revivals of parity chain populations and the os- cillatory behavior of the mean photon number are predicted. At the same time, photon number wave packets, propagating back and forth along parity chains, become incoherently mixed. Finally, we investi- gate numerically the effect of detuning on the validity of the analytical solution.