Correlated dynamics of droplets in a harmonic trap

We address the existence and dynamics of one-dimensional harmonically confined quantum droplets, that appear in two-component mixtures, deploying a nonperturbative approach. A transition from Gaussian-like to flat-top droplets occurs for varying intercomponent attraction in homonuclear settings, while flat-top signatures emerge at intermediate interactions due to beyond Lee-Huang-Yang correlations. For heteronuclear mixtures a pronounced mixing of the involved components takes place with the strongly interacting component exhibiting flat-top structures. An anti-bunching behavior is observed in the flat-top region, while two-body correlations are enhanced for larger interaction imbalances. Following quenches of the harmonic trap we monitor the development of the lowest-lying collective droplet excitations. The breathing mode is found to be unstable in the long time-evolution associated with the build-up of higher-lying excitations. Its frequency depends on the intercomponent attraction and it is found to be slightly reduced in the presence of correlations. In sharp contrast, the dipole motion of the droplet remains robust, while irregular dipole patterns are observed after the component collision in a species selective trap.