Characterization of Phase Rigidity in Non-Hermitian Acoustic Systems

By tuning of system parameters, a non-Hermitian system can be driven across a specific point in the parameter space, known as the exceptional point. At the exceptional point, the relevant eigenfrequencies of the system become degenerate, and the eigenvectors become parallel. Such behavior can be captured using a concept called phase rigidity. In this work, we present a theoretical analysis and experimental measurement of phase rigidities of a 2×2 and a 3×3 tight-binding non-Hermitian acoustic system. The 2×2 system is a well-known and well-characterized system that serves as a reference to show the effectiveness of our approach. The 3×3 system can produce an order-3 exceptional point at which three eigenmodes coalesce. Interestingly, we found that among the three eigenmodes, two approach the exceptional point with the same critical exponent and the same slope, whereas the third one has a different slope.