Walking droplets correlated at a distance

Bouncing fluid droplets can walk on the surface of a vibrating bath forming a wave-particle association. Walking droplets have many quantum-like features. Research efforts are continuously exploring quantum analogues and respective limitations. Here, we demonstrate that two oscillating particles (millimetric droplets) confined to separate potential wells exhibit correlated dynamical features, even when separated by a large distance. A key feature is the underlying wave mediated dynamics. The particles’ phase space dynamics is given by the system as a whole and cannot be described independently. Numerical phase space histograms display statistical coherence; the particles’ intricate distributions in phase space are statistically indistinguishable. However, removing one particle changes the phase space picture completely, which is reminiscent of entanglement. The model here presented also relates to nonlinearly coupled oscillators where synchronization can break out spontaneously. The present oscillator-coupling is dynamic and can change intensity through the underlying wave field as opposed to, for example, the Kuramoto model where the coupling is pre-defined. There are some regimes where we observe phase-locking or, more generally, regimes where the oscillators are statistically indistinguishable in phase-space, where numerical histograms display their (mutual) most likely amplitude and phase.