Direct Measurement of Topological Invariants and Nonlinear-Coupling-Induced Multistability in Actively Modulated Acoustic Cavity Systems

We present our recent advances in actively modulated acoustic cavity systems, which enable unprecedented control over topological and nonlinear wave phenomena. First, we demonstrate direct measurement of topological invariants, including the Zak phase and Chern number, through the temporal adiabatic evolution of bulk states in synthetic dimensions. This is realized via time-varying coupling in a single cavity, allowing extraction of Berry phases and even probing non-Abelian characteristics. Second, we introduce a nonlinear acoustic dimer with amplitude-dependent coupling, which exhibits a tunable quintic response and three dynamically stable states. Conventional sweeps produce asymmetric hysteresis, leaving the intermediate state inaccessible. However, by exploiting the reshaped phase-space geometry and a two-stage adiabatic protocol, we achieve complete and selective excitation of all stable states. Our work provides novel pathways for topological wave manipulation and programmable multistate control in classical wave systems.