Modulational instability and quantum droplets in a two-dimensional Bose-Einstein condensate

TL;DR

This paper investigates how quantum fluctuations induce modulational instability in a two-dimensional binary Bose-Einstein condensate, leading to the formation and dynamic evolution of quantum droplets.

Contribution

It demonstrates that quantum fluctuations can trigger instability below a certain density threshold and analyzes the resulting droplet dynamics in 2D BECs.

Findings

Quantum fluctuations induce instability below a density threshold.

Asymmetry in interactions reduces the growth rate of modulations.

Quantum droplets form and merge dynamically, decreasing in number over time.

Abstract

Modulational instability of a uniform two-dimensional binary Bose-Einstein condensate (BEC) in the presence of quantum fluctuations is studied. The analysis is based on the coupled Gross-Pitaevskii equations. It is shown that quantum fluctuations can induce instability when the BEC density is below a threshold. The dependence of the growth rate of modulations on the BEC parameters is found. It is observed that an asymmetry of the interaction parameters and/or initial densities of the components typically decreases the growth rate. Further development of the instability results in a break-up of the BEC into a set of quantum droplets. These droplets merge dynamically with each other so that the total number of droplets decreases rapidly. The rate of this decrease is evaluated numerically for different initial parameters.