Exploring Quantum Mechanical and Optical Analogies through Surface Gravity Water Waves

The investigation of analogies across various physical domains, including quantum
mechanics, nonlinear optics, and classical physics, offers a rich tapestry for
understanding the fundamental behaviors that govern the universe. Among these
explorations, the study of surface gravity water waves stands out for its capacity to
bridge the realms of quantum and classical physics, particularly through the lens of
wave-particle duality. This concept, central to quantum physics, posits that entities like
photons and electrons possess both wave-like and particle-like characteristics, a duality
also resonant in classical physics.
Our research delves into the theoretical and experimental exploration of these quantum
mechanical analogies within the context of hydrodynamics. Specifically, we focus on the
propagation dynamics of surface gravity water waves as they mimic the behaviors
predicted by the Schrödinger equation under certain conditions. Our initial foray into this
domain involved studying the propagation of Gaussian and Airy wave packets, leading
to the pioneering observation of the Kennard cubic phase [1]. Further exploration
allowed us to examine solitons within a linear potential [2], highlighting their unique
ability to maintain shape while accelerating.
Significantly, our work extends to the Talbot effect, where we not only confirmed its
occurrence in both amplitude and phase but also ventured into its nonlinear aspects,
marking the first observation of the fractional Talbot effect's absence due to nonlinear
medium interference [3]. Our current efforts are aimed at deepening the understanding
of quantum mechanics and surface wave analogies, focusing on phenomena such as
wave packet scattering from inverted oscillator potentials, quantum decoherence, and
the emulation of black holes in phase space.
Remarkably, our experimental framework has facilitated the measurement and analysis
of Bohm trajectories and quantum potentials across various wave packet configurations,
including multiple slit arrangements and Airy slits [4]. This has opened the door to
potentially observing the Wigner distribution of wave functions and related quantum
phenomena. Our recent discoveries also include the ability to simulate antireflection
temporal coatings and the diffractive focusing and guiding of waves, positioning our
research as a novel platform for elucidating complex optical system fundamentals and
quantum phenomena.