Study of Topological Phenomena Through Berry Phase in Classical Nonlinear Elastic Granules

The geometric of Berry phase concept, traditionally rooted in quantum mechanics, has been found to be increasingly significant in classical mechanics, particularly for understanding the dynamics of linear and nonlinear systems. In this study, we demonstrate the controlled accumulation of the Berry phase in a classical system using a two-level time-dependent elastic bit, analogous to a quantum bit, within a nonlinear environment generated by a two-granular network. The nonlinearity of the granular beads is modulated through the frequency and amplitude of external harmonic excitation, along with static preloading. By employing the orthonormal basis of the nonlinear responses and mapping the displacement coefficients in Bloch states, we reveal how time influences the manipulation of the elastic bit and its states. Our analytical and experimental investigations uncover the Berry phase's role in exposing the various topological characteristics of the classical granular network. This research establishes a crucial link between classical and quantum realms via the Berry phase of an elastic bit, with significant implications for decoherence-free and robust data transfer and information processing.