Observation of Floquet-Bloch Braids in Non-Hermitian Spatiotemporal Lattices.

The formation of nontrivial braid structures of complex energies enables a new topological classification beyond conventional topological band theory. In this Letter, we introduce the concept of braiding topology to dynamic systems and reveal novel Floquet-Bloch braids in non-Hermitian spatiotemporal lattices. This nonequilibrium braiding topology, closely related to the breakdown of continuous time translation symmetry, is characterized by an invariant derived from Floquet operators. In sharp contrast to static lattices, the Floquet-Bloch braids can be directly manipulated using temporal engineering, enabling an arbitrary braiding degree even in a two-band lattice without long-range hopping. Experimentally, we synthesize Floquet-Bloch bands in an acoustic platform with time-modulated unidirectional couplers. We not only realize a series of Floquet-Bloch braids with distinct topologies, but also observe the transition states featuring state-coalesced Floquet exceptional points. Our findings reveal a fundamental interplay between non-Hermiticity and Floquet engineering, and pave the way for experimentally exploring the rich and uncharted territory of nonequilibrium non-Hermitian physics.