Ideal Flat and Resolved SU(3) Landau Levels in Three Dimensions

Landau levels (LLs) are of great importance for understanding the quantum Hall effect and associated many-body physics. Recently, their three-dimensional (3D) counterparts, i.e., dispersionless 3D LLs with well-defined quantum numbers, have attracted significant attention but have not yet been reported. Here we theoretically propose and experimentally observe 3D LLs with a sharply quantized spectrum in a diamond acoustic lattice, where the eigenstates are characterized by SU(3) quantum numbers. The engineered inhomogeneous hopping strengths not only introduce pseudomagnetic fields that quantize the nodal lines into LLs but also provide three bosonic degrees of freedom, embedding a generic SU(3) symmetry into the LLs. Using a phased array of acoustic sources, we selectively excite distinct eigenstates within the degenerate LL multiplets and visualize their 3D eigenmodes. Importantly, our approach enables the precise reconstruction of SU(3) quantum numbers directly from eigenmode correlations. Our results establish SU(3) LLs as a tractable model in artificial platforms, and pave the way for synthesizing LLs with zero dispersion and countable quantum numbers in arbitrary dimensions.