Quantum droplets in three-dimensional Bose-Einstein condensates

TL;DR

This paper investigates the properties and dynamics of quantum droplets in three-dimensional Bose-Einstein condensates using variational and numerical methods, providing analytical and simulation insights into their behavior.

Contribution

It introduces a super-Gaussian trial function for variational analysis and explores the effects of periodic modulation on quantum droplet oscillations.

Findings

Super-Gaussian trial function effectively describes quantum droplets.

Analytical equations for variational parameters are derived.

Periodic modulation induces resonance oscillations or wave emission.

Abstract

The properties of 3D Bose-Einstein condensate have been studied with variational and numerical methods. In the variational approach, we use the super-Gaussian trial function, and it is demonstrated that this trial function gives a good approach for the descriptions of the quantum droplets. The analytical equations for the variational parameters are obtained. The frequency of small oscillations of quantum droplets near the equilibrium position is estimated. It is also found that periodic modulation of the coupling constants leads to the resonance oscillations of the quantum droplets parameters or emission of waves depending on the amplitude of the modulations. The predictions are supported by direct numerical simulation of governing equation.