Hong-Ou-Mandel-like two-droplet correlations

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics
• Hydrodynamic Quantum Analogs

Background:

• Walking droplets on vibrating baths mimic quantum mechanical systems.
• Interactions between droplets are crucial for understanding complex fluid behaviors.
• Previous studies have explored single droplet dynamics; pair correlations are less understood.

Purpose of the Study:

• To numerically investigate the pair correlations between two in-phase walking droplets.
• To quantify the probability of forming two-droplet bound states.
• To identify and characterize different types of observed droplet pair correlations.

Main Methods:

• Numerical simulation of two in-phase droplets on a vibrating fluid bath.
• Launching droplets towards a common intersection point to observe wave overlap.
• Quantifying pair correlation by measuring the probability of bound states at late times.

Main Results:

• Observed three distinct types of two-droplet correlations: promenading, orbiting, and chasing pairs.
• Demonstrated that droplet pairing probability depends on initial conditions and system parameters.
• Identified parameter regimes where droplets become correlated or remain uncorrelated.

Conclusions:

• Two walking droplets can form stable bound states through carrier wave interactions.
• The nature and likelihood of droplet pairing are sensitive to initial path differences.
• Findings provide a foundation for studying complex, correlated behaviors in many-droplet systems.