Realization of 3D all-flat bands in acoustic Fock-state lattices

Flat bands have emerged as a cornerstone of contemporary condensed matter physics, with promising applications in photonic and phononic crystals that have garnered significant attention. In three-dimensional (3D) crystals, flat bands can be realized through Landau levels (LLs) induced by synthetic magnetic fields with crystal lattice distortions, forming partially flat bands that nevertheless become dispersive around the boundaries and surfaces. However, the realization of ideal all-flat (non-dispersive) LLs in 3D systems has remained elusive thus far. Here, we propose a general model to generate all-flat LLs in 3D systems and experimentally demonstrate the exotic wave propagation behavior with 3D acoustic Fock-state lattices. Notably, this framework can be generalized to other wave systems, such as photonics and electronics. Our findings not only resolve controversies regarding the existence of all-flat (non-dispersive) LLs, but also advance the exploration of flat bands and quantized physics in classical wave systems, providing new possibilities for high-Q detection and energy harvesting applications.