Quantum Mechanical and Optical Emulations and Simulations with Surface Gravity Waves

Exploring the correspondences between classical and quantum systems provides valuable insights across various domains of physics, including optics, acoustics, condensed matter, and

particle physics. Specifically, surface gravity waves offer fascinating analogies to quantum mechanics, particularly in demonstrating wave-particle duality—a fundamental concept

where quantum entities exhibit both wave-like and particle-like behaviors. This research delves into both theoretical and experimental aspects of quantum mechanical analogies using

hydrodynamics, focusing on the propagation dynamics of surface gravity waves that mirror the behaviors predicted by the Schrödinger equation under specific conditions. Initial studies

centered on Gaussian and Airy wave packets, leading to the first observation of the Kennard cubic phase. Subsequent investigations explored the dynamics of solitons in linear potentials

and the Talbot effect, revealing novel phenomena in both amplitude and phase, including the suppression of fractional Talbot effects in nonlinear media. Current efforts extend to

examining deeper quantum analogies with surface waves, such as wave packet scattering from inverted oscillator potentials, quantum decoherence, and ballistic behaviors. Moreover, recent

advancements in our experimental setup have enabled the study of Bohm trajectories, quantum potentials, and the Wigner distribution, alongside innovative emulations of temporal

antireflection coatings and wave focusing techniques. This research not only enhances our understanding of complex optical systems but also establishes a versatile platform for studying

foundational quantum phenomena.