Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach

Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. This theory shows that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.