# Statics and dynamics of a self-bound dipolar matter-wave droplet

## TL;DR

This paper investigates the static and dynamic behaviors of self-bound dipolar matter-wave droplets, revealing their soliton-like collisions and the formation of droplet molecules under specific conditions, using analytical and numerical methods.

## Contribution

It introduces a detailed analysis of dipolar droplet collisions, including the formation of droplet molecules, based on a variational approach and Gross-Pitaevskii simulations.

## Key findings

- Droplets behave like quantum solitons during high-velocity collisions.
- Small velocity collisions depend on dipolar orientation, leading to coalescence or repulsion.
- Droplet molecules form when collisions occur along the polarization axis at low velocities.

## Abstract

We study the statics and dynamics of a stable, mobile, self-bound three-dimensional dipolar matter-wave droplet created in the presence of a tiny repulsive three-body interaction. In frontal collision with an impact parameter and in angular collision at large velocities {along all directions} two droplets behave like quantum solitons. Such collision is found to be quasi elastic and the droplets emerge undeformed after collision without any change of velocity. However, in a collision at small velocities the axisymmeric dipolar interaction plays a significant role and the collision dynamics is sensitive to the direction of motion. For an encounter along the $z$ direction at small velocities, two droplets, polarized along the $z$ direction, coalesce to form a larger droplet $-$ a droplet molecule. For an encounter along the $x$ direction at small velocities, the same droplets stay apart and never meet each other due to the dipolar repulsion. The present study is based on an analytic variational approximation and a numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of $^{52}$Cr atoms.