Dragging A Defect in a Droplet Bose-Einstein Condensate

TL;DR

This paper investigates the behavior of quantum droplets with defects across 1D, 2D, and 3D, analyzing stability, bifurcations, and dynamics, revealing connections to solitons and vortical structures.

Contribution

It provides a comprehensive analysis of defect-induced states in quantum droplets, including bifurcation diagrams and stability in multiple dimensions, with no existing analytical solutions.

Findings

Identification of saddle-center bifurcations as defect parameters vary

Construction of systematic bifurcation diagrams for quantum droplets

Connection of defect states to solitonic and vortical patterns

Abstract

In the present work we consider models of quantum droplets in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations and dynamics in 1D, 2D and 3D settings. In the absence of an analytical solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed systematically, and the unstable states, as well as the dynamics past the existence of stable states is monitored. The connection of the resulting states with dark solitonic patterns in 1D, vortical states in 2D and vortex rings in 3D is accordingly elucidated.