Engineering nonequilibrium steady states through Floquet Liouvillians

We experimentally study the transient dynamics of a dissipative superconducting qubit under periodic drive towards its nonequilibrium steady states. The corresponding stroboscopic evolution, given by the qubit states at times equal to integer multiples of the drive period, is determined by a (generically non-Hermitian) Floquet Liouvillian. The drive period controls both the transients across its non-Hermitian degeneracies and the resulting nonequilibrium steady states. These steady states can exhibit higher purity compared to those achieved with a constant drive. We further study the dependence of the steady states on the direction of parameter variation and relate these findings to the recent studies of dynamically encircling exceptional points. Our work provides a new approach to control non-Hermiticity in dissipative quantum systems and presents a new paradigm in quantum state preparation and stabilization.