  The valley-polarized quantum anomalous Hall (VQAH) state, which forwards a
strategy for combining valleytronics and spintronics with nontrivial topology,
attracts intensive interest in condensed-matter physics. So far, the explored
VQAH states have still been limited to magnetic systems. Here, using the
low-energy effective model and Floquet theorem, we propose a different
mechanism to realize the Floquet VQAH state in nonmagnetic heterobilayers under
light irradiation. We then realize this proposal via first-principles
calculations in transition metal dichalcogenide heterobilayers, which initially
possess the time-reversal invariant valley quantum spin Hall (VQSH) state. By
irradiating circularly polarized light, the time-reversal invariant VQSH state
can evolve into the VQAH state, behaving as an optically switchable topological
spin-valley filter. These findings not only offer a rational scheme to realize
the VQAH state without magnetic orders, but also pave a fascinating path for
designing topological spintronic and valleytronic devices.
