Quantum droplets in Bose-Bose mixtures

Abstract

Most recent sensational breakthrough in the eld of ultracold atomic quantum gases is the creation of self-bound droplet state. This exotic phase of matter which can be formed in dipolar condensates and binary Bose mixtures, results from the competition between an attractive mean- eld energy and the repulsive Lee-Huang-Yang correction. This thesis looks to answer the question of e ects of higher-order quantum and thermal uctuations on the stabilization of self-bound droplets in Bose-Bose mixtures. Within the Hartree-Fock-Bogoliubov theory we calculate the ground-state energy, the droplet equilibrium density, the depletion and anomalous density of the droplet as well as the critical temperature as a function of the relevant parameters. Our ndings for the ground-state energy are compared with recent available analytical predictions and di usion Monte Carlo simulations and excellent agreement is found. We compute the density pro les and breathing modes of the droplet of this novel state of matter by numerically solving the underlying generalized nitetemperature Gross-Pitaevskii equation. This latter is derived selfconsistently from our theory using the local density approximation. We study also in this thesis the bulk and surface properties of ultradilute self-bound quantum droplets in a heteronuclear Bose-Bose mixture. Within the realm of the Hartree-Fock-Bogoliubov theory, we calculate beyond the Lee-Huang-Yang corrections to the ground-state energy, the droplet equilibrium density, the surface tension, and the critical number of particles. Our predictions coincide perfectly with recent di usion Monte Carlo simulation and density functional theory method.