Dynamics of one-dimensional quantum droplets

TL;DR

This paper investigates the structure and collision dynamics of one-dimensional quantum droplets in binary Bose gases, revealing regimes of Gaussian-shaped small droplets and large puddles, with insights into their stability and excitation modes.

Contribution

It provides a detailed analysis of droplet behavior, including collision outcomes and stability criteria, using numerical simulations and variational approximations.

Findings

Small droplets exhibit quasi-elastic, soliton-like collisions.

Large droplets can merge or fragment depending on velocity.

The breathing mode frequency matches variational predictions.

Abstract

The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large `puddles' with a broad flat-top plateau. Small droplets collide quasi-elastically, featuring the soliton-like behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.