Transport properties comparison between walking droplets in a rotating bath and electrons in two-dimensional systems with perpendicular magnetic field

Details

Supervisors

Hackens, Benoît

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil électricien, à finalité spécialisée

Abstract

The walking droplet experiment gained interest over the last decades because it is known as the first example of a macroscopic pilot-wave system that exhibits behaviours thought to be exclusive to the microscopic quantum realm. Until now, the walking droplet topics were mainly focused about its behaviour characterization both in fluid mechanics and mathematical modeling, and also about the comparison of its behaviour with particles showing wave-particle duality such as electrons. However, no reported experiments have paid attention to walker transport properties through cavities with input and output leads, that could be comparable to transport properties of electrons. Consequently, the objective of this master thesis is to analyze the transport properties of walking droplets through two types of cavity that undergo a constant angular velocity, analog to magnetic field application on two-dimensional system. The two cavities are an analog quantum ring and a Bunimovich stadium billiard, each interesting for different known phenomena in the electronic world. Indeed, the quantum ring is particularly well known for exhibiting Aharonov-Bohm effect while the Bunimovich stadium billiard is known for showing scars in the quantum world, as opposed to the classical world that presents chaotic behaviours. To fulfill this objective, the experimental setup developed by O.Leblanc two years ago was the starting point, mainly modified to include bath rotation control. The current setup includes the following components : the two baths that can be fixed on the membrane of a loudspeaker for the vertical acceleration, a 3-axis accelerometer, a droplet generator, a stepper motor on which the loudspeaker is nested and a fixed camera recording top view images of the droplet horizontal motion, post-processed by tracking algorithms. The imperfect electrical contacts between the stationary and rotating structure shows amplitude variations of ± 120[mg] that guided the choice of low memory experiments, with a Faraday instability threshold found at Γ_F = 4.03 [g]. For both baths, the walking droplet transmission shows a global increase to a maximum transmission probability with the angular velocity increase of the bath, with some transmission fluctuations. The ring-shaped bath fluctuations with angular velocity are thought to be related to particular interactions at the 'T-junction' both to enter or to exit the ring. Yet, the stadium-shaped bath fluctuations are rather due to the orbital radius of the walking droplet that decreases with angular velocity, guiding the walking droplet trajectory and influencing the transmission.