Wave mediated interaction in a lattice of bouncing drops

Abstract

This project’s larger goal involves devising an experimental method to investigate links between a lattice of bouncing drops and the Ising machine. The coupling between droplets plays a crucial role in this aspect and the work carried out here encapsulates some major features pertaining to this interaction between droplets. An Ising machine is an artificial system of spins based on the Ising model, which describes the energy of a set of interacting constituent spin like elements with bi-stable states. Combinatorial optimization problems are a large class of problems which involve optimizing a certain quantity from a set of discrete elements and they can be mapped to the Hamiltonian function of the Ising model. These problems belong to the class of NP-hard problems for which computational complexity grows as a power law with each new added element. The purpose of building an Ising machine is to provide an architecture which can efficiently solve such problems by finding the ground state of its constituent elements. Previously, interacting coupled parametric oscillators have been proposed as a possible implementation of an Ising machine. The ground state can be efficiently determined by slowly increasing the excitation until each oscillator reaches a bi-stable state which is determined by its interactions with the other oscillators. A set of bouncing droplets on a vertically vibrated bath is a good candidate for an Ising machine. Each droplet can be considered as a parametrical oscillator which is controlled by the vibration of the bath. These droplets undergo period doubling above a given excitation threshold which defines a bi-stable state defined by their phase. These ‘artificial spins’ interact with each other through the waves that they emit on the bath. This interaction can be tuned by changing the distances between droplets.