Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.

从科学和工程的角度来看，激光技术已经发展并加速了光诱导非平衡物理学。Floquet 工程，即通过时间周期驱动控制材料特性和功能，处于光与物质相互作用的量子物理学的最前沿。然而，它仅限于理想的无耗散系统。将 Floquet 工程扩展到各种材料需要了解在周期性驱动和能量耗散的平衡中出现的量子态。在这里，我们通过关注高频驱动和与时间无关的 Lindblad 型耗散系统，得出周期性驱动耗散系统中非平衡稳态 (NESS) 的一般描述。我们的公式正确地描述了 NESS 的时间平均、涨落和对称性，并且可以在数值计算中有效地进行计算。这种方法将在从原子和分子到介观系统和凝聚态物质的广泛耗散量子系统中的 Floquet 工程中发挥基础作用。