Formation Dynamics of Quantum Droplets for Homonuclear and Heteronuclear Mixtures

Abstract: Great effort has been invested over the past decade in studying the properties of quantum droplets, a phase of bosonic quantum matter that arises as a consequence of the fluctuating Lee-Huang-Yang correction. However, the dynamics of droplet formation for heteronuclear Bose mixtures is partially understood. Here, we numerically analyze the formation process for homonuclear and heteronuclear boson mixtures in one dimension using a tight-binding model and real-time evolution. A systematic sweep of interaction strengths, mass ratios, and initial conditions allows us to characterize quantitative criteria for droplet formation and equilibration. We find that the energy contribution of the LHY correction dominates the energetic profile of the droplets formed, with the deepest binding occurring for mass ratios $m_2/m_1 \in [1.2,2.0]$. Breathing oscillations are observed, and the low equilibration rate is consistent with the restricted nature of the phase space for one-dimensional systems; the oscillation frequency is found to have a very weak correlation to the interaction strengths. For the simulation, Gaussian over discrete initial conditions are clearly favorable to the formation of droplets. The results contained herein provide rich insight into the dynamical nature of quantum droplet physics.