One-Dimensional Quantum Droplets

I will discuss a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. I will specifically focus on the excitation spectrum properties. The droplet properties are governed by a single control parameter proportional to the particle number. For large values of this parameter the solution features the flat-top, droplet-like shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk. With decreasing control parameter these modes move to the continuum, sequentially crossing the particle-emission threshold. A notable exception is the breathing mode which is found to be always bound. As the control parameter tends to minus infinity, this ratio tends to one and the droplet transforms into the soliton solution of the integrable cubic GPE. The preprint is available as arXiv:2003.05803.