Transient and nonequilibrium steady state of a periodically driven dissipative qubit

Floquet engineering can significantly modify the energy spectra of quantum systems and create novel states of matter, such as discrete time crystals observed in periodically driven many-body-localized systems. The interplay of periodic drive and energy dissipation of quantum systems further enriches the quantum dynamics and leads to nonequilibrium steady states. In this work, we study the transient dynamics of a periodically driven dissipative qubit towards its nonequilibrium steady state, which is determined by a (generically non-Hermitian) Floquet Liouvillian. The stroboscopic evolution, given by the qubit states at times equal to integer multiples of the drive period, exhibits a transition from oscillatory decay to exponential decay, indicating the occurrence of an exceptional point degeneracy of the Floquet Liouvillian. We further observe chiral nonequilibrium steady states by varying the drive parameters. Our work provides a new approach to studying exceptional points in dissipative quantum systems and may benefit state preparation and stabilization through Floquet engineering.