Formation Dynamics of Quantum Droplets for Homonuclear and Heteronuclear Mixtures

Abstract

Significant efforts have been devoted to studying the properties of quantum droplets, an ultra low-temperature phase of bosonic quantum matter that emerges as a consequence of the Lee-Huang-Yang fluctuating correction. However, the temporal dynamics of droplet formation for heteronuclear bosonic mixtures is only partially understood. Here, we numerically analyze the droplet formation process for homonuclear and heteronuclear binary bosonic mixtures in one dimension, using a tight-binding model and real-time evolution with a novel, highly robust integration algorithm. We proceed with a systematic scan of interaction intensities, mass ratios, and initial conditions that allows us to characterize quantitative criteria for droplet formation and equilibrium prospects. Noticeably, most droplets readily form across the entire parameter space, although only a small fraction achieves a stable equilibrium configuration within the simulation horizon. We attribute this equilibrium deficiency to damping from a breathing mode, which we extract directly from the width oscillations at late times. The Lee-Huang-Yang contribution supplies essentially the entire binding energy, while, at late times, the density profile of the equilibrated subset is better described by a soliton-like shape rather than the flat-topped profiles characteristic of larger droplets. Referring to the energy of the free-atom band, the binding energy grows super-extensively with the number of atoms as $E_{\text{bind}} \propto N^{1.6}$. Heteronuclear droplets bind more strongly as the mass ratio between their components increases and exhibit breathing oscillations that are greater than those of their homonuclear counterparts, which is consistent with the role of mass-imbalanced kinetic terms. Our analysis provides a methodological framework for interpreting real-time quantum droplet simulations.