Realization of Berry Phase in Classical Nonlinear Granular Network Using Quantum Analogue Theory*

The investigation of the Berry phase in classical and quantum systems has significantly advanced the field of quantum information science and technology. The Berry phase, which arises from an adiabatic cyclic process, can interpret system dynamics. We illustrate the generation of a Berry phase in an elastic bit, a quantum counterpart of a two-level system. A Hertz-type nonlinearity is created by harmonically operating the system in a classical nonlinear system with two single-point contact granules to study the elastic bit's creation. We demonstrate the effect of the driving parameters, where the external force can control the nonlinearity of the granules, creating time independent and dependent elastic bits. The time-independent coherent superposition of states is manipulated by tuning external excitation in a linearized system. We calculate the quantized Berry phase by mapping it on the Bloch sphere. Equal superposition of elastic bit states results in the nontrivial Berry phase of π. In contrast, the zero Berry phase represents pure states, where superpositions might have values other than 0 or π. Nonlinearity creates time-dependent evolution of superposition of states. We exhibit the nonlinearity effect of the experimental development of the Berry phase, in which coherent states exhibit time dependence. These features are essential in topological computing, particularly in non-abelian computation, where a Berry phase is acquired through braiding.