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arXiv:2109.14931 · Atoms

Static Impurities in a Weakly Interacting Bose Gas

G. Panochko, V. Pastukhov

Published Feb 8, 2022• 10 citations
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Abstract

We present a comprehensive discussion of the ground-state properties of dilute D-dimensional Bose gas interacting with a few static impurities. Assuming the short-ranged character of the boson-impurity interaction, we calculated the energy of three- and two-dimensional Bose systems with one and two impurities immersed.
DOI
10.3390/atoms10010019

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An impurity in a Bose gas is commonly referred to as a Bose polaron. For a dilute Bose gas, its properties are expected to be universal, i.e., dependent only on a few parameters characterizing the boson-impurity interactions. It has been known for some time that when boson-impurity interactions are weak, the properties of the polaron depend only on the scattering length of these interactions. In this paper, which accompanies Phys. Rev. Lett. 126, 123403 (2021) (where some of these results have already been reported), we examine stronger boson-impurity interactions, keeping their range finite. We demonstrate that for attractive interactions between impurity and the bosons up to and including the unitary point, all static properties of a Bose polaron in a dilute Bose gas can be calculated in terms of the scattering length and an additional parameter that characterizes the range of the impurity-boson interactions. Our approach is valid if this parameter does not deviate too much from the scattering length of intraboson interactions, with the precise criterion given in the text. We produce explicit expressions for the energy and other properties of a polaron for the case when the impurity-boson scattering length is tuned to unitarity, and we also provide the first correction away from it.
In this thesis we investigate the properties of impurities immersed in a dilute Bose gas at zero temperature using quantum Monte-Carlo methods. The interactions between bosons are modeled by a hard sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We calculate the binding energy, the effective mass and the pair correlation functions of a impurity along the attractive and the repulsive polaron branch. In particular, at the unitary limit of the impurity-bosons interaction, we find that the binding energy is much larger than the chemical potential of the bath signaling that many bosons dress the impurity thereby lowering its energy and increasing its effective mass. We characterize this state by calculating the bosons-boson pair correlation function and by investigating the dependence of the binding energy on the gas parameter of the bosonic bath. We also investigate the ground-state properties of M impurities in a Bose gas at T=0. In particular, the energy and the phase diagram by using both quantum Monte-Carlo and mean field methods.
We present a theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground-state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.