Hydrodynamic Aharonov–Bohm Effect and Time-Varying Vortex-Induced Phases

The Aharonov–Bohm effect is a major feature in quantum mechanics in that it affirms the physical reality of the electromagnetic vector potential. It arises when charged particles encircle a region of confined magnetic flux—such as a solenoid—without ever encountering the magnetic field. Despite the absence of Lorentz forces in the accessible region, the presence of the vector potential leads to a measurable phase shift in the particle's wavefunction, which in turn alters the particle energy.

Here, we construct a hydrodynamic analog of the Aharonov–Bohm effect using pilot-wave dynamics. In our experiment, a central vortex serves as the analog of the confined magnetic flux. The walking droplet moves within an annular domain encircling the vortex core, shielded from the vortex by subsurface topography. While the drop does not interact directly with the vortex, its pilot-wave does, thereby altering the droplet’s momentum. The droplet is thus subjected to a nonlocal phase shift akin to that observed in the quantum Aharonov–Bohm effect. This analogy offers new insights into the relationship between the phase of the pilot wave in pilot-wave hydrodynamics and the phase of the quantum wavefunction.

Extending this paradigm, we introduce a time-dependent vortex strength, dynamically varying the effective vector potential experienced by the droplet. This modulation leads to a time-dependent phase accumulation, enabling the exploration of a variety of new analogies with quantum phenomena.