Hong-Ou-Mandel-like two-droplet correlations

TL;DR

This study numerically investigates two-droplet correlations on a vibrating bath, revealing various pairing behaviors and their dependence on initial conditions, which advances understanding of hydrodynamical quantum analogs.

Contribution

It introduces a numerical analysis of two-droplet correlations, identifying different pairing types and their dependence on initial conditions in hydrodynamical systems.

Findings

Identified three types of droplet correlations: promenading, orbiting, chasing.

Observed parameter-dependent correlation behaviors, including bound states.

Provided insights into many-droplet behaviors in hydrodynamical quantum analogs.

Abstract

We present a numerical study of two-droplet pair correlations for in-phase droplets walking on a vibrating bath. Two such walkers are launched towards a common origin. As they approach, their carrier waves may overlap and the droplets have a non-zero probability of forming a two-droplet bound state. The likelihood of such pairing is quantified by measuring the probability of finding the droplets in a bound state at late times. Three generic types of two-droplet correlations are observed: promenading, orbiting and chasing pair of walkers. For certain parameters, the droplets may become correlated for certain initial path differences and remain uncorrelated for others, while in other cases the droplets may never produce droplet pairs. These observations pave the way for further studies of strongly correlated many-droplet behaviors in the hydrodynamical quantum analogs of bouncing and walking droplets.