On the ground state of one-dimensional quantum droplets for large chemical potentials

In the present work we revisit the problem of the quantum droplet in atomic Bose–Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas–Fermi (TF) limit. We consider the problem as being separable into 3 distinct regions: an inner one, where the TF approximation is valid, a sharp transition region where the density abruptly drops towards the (vanishing) background value and an outer region which asymptotes to the background value. We analyze the spatial extent of each of these regions, and develop a systematic effective description of the rapid intermediate transition region. Accordingly, we derive a uniformly valid description of the ground state that is found to accurately match our numerical computations. As an additional application of our considerations, we show that this formulation allows for an analytical approximation of excited states such as the (trapped) dark soliton in the large density limit.