The notion of berry phase in classical quantum analogous system

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The geometric or Berry phase has become essential in bridging the classical and quantum fields. These phases arise from the cyclic change of the system in a specific path. A quantum analogous classical system is considered to analyze the Berry phase through the evolution of the superposition of states. A classical granular system driven harmonically can create an elastic bit equivalent to a quantum bit, which is manipulated through the driver's frequency, amplitude, and static precompression. The granular system is adaptable to harmonic excitation due to the Hertz-type contact, resulting in different responses, from nonlinear to linearized. We analyze the Berry phase in both cases, where the elastic bit can be manipulated by varying the external excitation, and in a nonlinear system, time changes the superposition of states in the Hilbert space. This results in the accumulation of the Berry phase in time. We show the accumulation of the Berry phase both theoretically and experimentally. This study is important, as the Berry phase accumulation in a classical system shows its uses in topological computing. The Berry phase proves that the linearized and nonlinear systems are decoherence-free, resulting in a powerful tool for information processing.