Quasi-one-dimensional harmonically trapped quantum droplets

TL;DR

This paper provides a theoretical analysis of one-dimensional quantum droplets in a trapped Bose-Bose mixture, exploring their ground and excited states, stability, and transition to soliton-like structures as trapping strength varies.

Contribution

It introduces a systematic study of localized modes in quantum droplets within a harmonic trap, including stability analysis and the transition to soliton-like states.

Findings

Ground and excited states bifurcate from harmonic oscillator eigenstates.

Excited states are unstable near the linear limit but stabilize at higher particle numbers.

Quantum droplets can be transformed into soliton-like states by reducing trapping strength.

Abstract

We theoretically consider effectively one-dimensional quantum droplets in a symmetric Bose-Bose mixture confined in a parabolic trap. We systematically investigate ground and excited families of localized trapped modes which bifurcate from eigenstates of the quantum harmonic oscillator as the number of particles departs from zero. Families of nonlinear modes have nonmonotonous behavior of chemical potential on the number of particles and feature bistability regions. Excited states are unstable close to the linear limit, but become stable when the number of particles is large enough. In the limit of large density, we derive a modified Thomas-Fermi distribution. Smoothly decreasing the trapping strength down to zero, one can dynamically transform the ground state solution to the solitonlike quantum droplet, while excited trapped states break in several moving quantum droplets.