Ground state and dynamics of one-dimensional quantum droplets

Quantum droplets—arising from the delicate balance between repulsive and attractive interactions—continue to be of significant interest in the study of ultracold atomic systems. In this work, we revisit the ground-state properties and collective dynamics of one-dimensional quantum droplets. We identify a critical effective particle number,, at which the superfluid fraction exhibits a distinct inflection point, indicating a structural transition in the ground state. For, the density profile is sharply peaked, whereas for, it flattens into a plateau-like shape well-approximated by the Thomas–Fermi model. Additionally, we show that super-Gaussian functions provide excellent fits to the ground-state density profiles, offering a simple and accurate modeling approach. To study the system’s dynamical behavior, we develop an analytical framework for quantum droplets subjected to a periodic lattice potential. In the weak-lattice limit (), the excitation spectrum reveals a Goldstone gapless phonon mode, characteristic of superfluidity. However, at low densities, the inclusion of Lee–Huang–Yang corrections leads to phonon instabilities, consistent with the transition from a peak- to a plateau-like ground state. In the strong-lattice regime (large), a gap opens in the lowest excitation modes, suggesting a crossover from a superfluid to a Mott-insulating phase. Our findings should shed light on key aspects of a low-dimensional quantum droplet.