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We describe the dynamics of a qubit interacting with a bosonic mode coupledto a zero-temperature bath in the deep strong coupling (DSC) regime. We providean analytical solution for this open system dynamics in the off-resonance caseof the qubit-mode interaction. Collapses and revivals of parity chainpopulations and the oscillatory behavior of the mean photon number arepredicted. At the same time, photon number wave packets, propagating back andforth along parity chains, become incoherently mixed. Finally, we investigatenumerically the effect of detuning on the validity of the analytical solution.

Solvable model of dissipative dynamics in the deep strong coupling regime