Impurity in a Bose-Einstein condensate: study of the attractive and repulsive branch using quantum Monte-Carlo methods

摘要

We investigate the properties of an impurity immersed in a dilute Bose gas atzero temperature using quantum Monte-Carlo methods. The interactions betweenbosons are modeled by a hard sphere potential with scattering length $a$,whereas the interactions between the impurity and the bosons are modeled by ashort-range, square-well potential where both the sign and the strength of thescattering length $b$ can be varied by adjusting the well depth. Wecharacterize the attractive and the repulsive polaron branch by calculating thebinding energy and the effective mass of the impurity. Furthermore, weinvestigate structural properties of the bath, such as the impurity-bosoncontact parameter and the change of the density profile around the impurity. Atthe unitary limit of the impurity-boson interaction, we find that the effectivemass of the impurity remains smaller than twice its bare mass, while thebinding energy scales with $\hbar^2n^{2/3}/m$, where $n$ is the density of thebath and $m$ is the common mass of the impurity and the bosons in the bath. Theimplications for the phase diagram of binary Bose-Bose mixtures at smallconcentrations are also discussed.