Self-bound quantum droplets: ground state and excitations

Abstract

This project aims to study the ground state properties and excitations of self-bound quantum droplets. The ground state is obtained by numerically solving the extended Gross-Pitaevskii equation, which takes into account quantum fluctuations. Then, using a Gaussian variational ansatz for the ground state, we calculate the values of the number of particles for which the droplet is metastable, obtaining results that agree with the numerical calculations. Furthermore, to study the excited states, we use the Bogoliubov-de Gennes approximation. This approximation assumes small oscillations of the wave function around the ground state. Once obtained the Bogoliubov equations, we solve them numerically to analyze the first excited state, the breathing mode. The results show that it is a bulk mode since the perturbation starts at the core of the droplet.