Quasi-one-dimensional harmonically trapped quantum droplets

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.