Toward Classical Qubit Analogues: Phi-Bit Control in Coupled Acoustic Waveguides

Classical platforms that reproduce selected features of quantum behavior can provide useful testbeds for information-processing concepts. In this work, we develop and validate a theoretical model for phi-bits, which are nonlinear phase-encoded modes that serve as classical counterparts of qubit-like states, in a system of three coupled finite acoustic waveguides. A discrete mass-spring representation is used to capture the experimentally observed continuous phase variation of low-order combination modes generated under dual-frequency driving. The model includes damping, boundary effects, and nonlinear end-spring interactions, allowing us to track the dependence of phi-bit phase evolution on the driving frequency. For well-isolated modes with high signal quality, the predicted phase behavior, obtained from linear combinations of the two driving phases, shows good qualitative agreement with experiment. We further examine the role of higher-order nonlinear terms, showing that although they broaden the range of accessible responses, they may also weaken linear phase relations unless the spring parameters are properly rescaled in nondimensional form. Overall, this framework provides practical guidance for identifying robust phi-bits, optimizing frequency-sweep strategies, and extending the model to different material systems and geometries. These results highlight the potential of classical nonlinear acoustic lattices as controllable platforms for phase-based logic and quantum-inspired information processing.