Spin lattices of walking droplets

Giuseppe Pucci
Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) ­ UMR 6251, F­35000 Rennes, France

A droplet bouncing on the surface of a vibrating liquid bath can self-propel across the surface through interaction with the wave field it generates by bouncing. These walking droplets or “walkers” comprise a droplet and its guiding wave, and have been shown to exhibit several behaviors analog to quantum systems. Most analogs consider a single walker interacting with boundaries or experiencing external forces. Controlling multiple walkers is challenging as their continuous wave-mediated interactions usually lead to pair bound states and droplet-droplet coalescence. Here I show that multiple walkers can be manipulated by designing the bottom topography of the vibrating bath as a lattice composed of deeper regions separated by shallow regions. Specifically, I show that circular wells at the bottom of the fluid bath encourage individual droplets to walk in clockwise or counter-clockwise direction along circular trajectories centered at the lattice sites. A thin fluid layer between the wells enables wave-mediated interactions between neighboring walkers resulting in ordered rotation dynamics across the lattice. When the pair coupling is sufficiently strong, interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or anti-ferromagnetic order. In addition, an anti-ferromagnetic to ferromagnetic transition is obtained when the whole bath is rotating. Our experiments demonstrate the spontaneous emergence of collective behavior of walkers that mimic spin lattices.

This work has been done at Massachusetts Institute of Technology with Pedro J. Saenz, Sam E. Turton, Alexis Goujon, Rodolfo R. Rosales, Jörn Dunkel and John W. M. Bush.