Quantum droplets in random potentials

Abstract

One of the important achievements in the eld of ultracold atoms is the recent prediction and observation of ultradilute quantum liquid droplets, a new quantum state of matter. Quantum droplet originates due to the subtle balance between the attractive mean- eld force and the repulsive force provided by the Lee-Huang-Yang quantum uctuations. This thesis aims rst to study large bulk properties of self-bound quantum droplets of Bose mixtures in weak disorder potentials, and second introduces - nite size e ects within a generalized disorder-dependent Gross-Pitaevskii equation. Our investigation encompassed the examination of both uncorrelated and correlated disorders in three dimensions at zero and nite temperatures. We look in particular at how the intriguing interplay of the disorder, interspecies interaction and the Lee-Huang-Yang quantum uctuations a ect the formation and the stability of such a novel state of matter. New useful analytic expressions for the equation of state, equilibrium density, glassy fraction, depletion, and the anomalous density of the droplet are obtained in terms of the disorder parameters using the Bogoliubov-Huang-Meng theory. Our results reveal the signi cant role played by the strength and correlations of disorder in the stability and in self-evaporation phenomenon of the droplet state. At nite temperature, we analyze the free energy and the critical temperature above which the droplet evaporates. It is found that the competition between the thermal uctuations and disorder may strongly destabilize the droplet and completely destroy it above a certain critical temperature. We discuss the validity conditions of the present Bogoliubov theory. Furthermore, the structure and dynamics of the nite size quantum droplet in a three-dimensional random potential are explored by numerically solving the corresponding disorderdependent Gross-Pitaevskii equation. We also investigate the lowest-lying excitations of self-bound droplets employing a variational method. Our predictions point out that the peculiar interplay of the disorder and the repulsive Lee-Huang-Yang corrections leads to deform the atomic density in the at-top plateau region and to modify the collective modes of the self-bound droplet. Finally, our study is extended to one-dimensional geometry. We describe the bulk properties of disordered droplets using the aforementioned Bogoliubov method. We then conduct a numerical study in the purpose of revealing the impacts of weak random external potentials in two physically di erent regimes are identi ed, namely: small droplets of an approximately Gaussian shape and large droplets with a broad at-top plateau.