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arXiv:1703.10390 · Condensed Matter Physics

Behavior of the impurity atom in a weakly-interacting Bose gas

G. Panochko, V. Pastukhov, I. O. Vakarchuk

Published Mar 1, 2017• 9 citations
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Abstract

We studied the properties of a single impurity atom immersed in a dilute Bose condensate at low temperatures.In particular, we perturbatively obtained the momentum dependence of the impurity spectrum and damping.By means of the Brillouin-Wigner perturbation theory we also calculated the self-energy both for attractive and repulsive polaron in the long-wavelength limit.The stability problem of the impurity atom in a weakly-interacting Bose gas is also examined.

DOI
10.5488/cmp.20.13604

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We studied the properties of a single impurity atom immersed in a dilute Bose condensate at low temperatures.In particular, we perturbatively obtained the momentum dependence of the impurity spectrum and damping.By means of the Brillouin-Wigner perturbation theory we also calculated the self-energy both for attractive and repulsive polaron in the long-wavelength limit.The stability problem of the impurity atom in a weakly-interacting Bose gas is also examined.
We study the properties of an impurity immersed in a weakly interacting Bose gas, i.e., of a Bose polaron. In the perturbatively tractable limit of weak impurity-boson interactions many of its properties are known to depend only on the scattering length. Here we demonstrate that for strong (unitary) impurity-boson interactions all quasiparticle properties of a heavy Bose polaron, such as its energy, its residue, its Tan's contact, and the number of bosons trapped nearby the impurity, depend on the impurity-boson potential via a single parameter characterizing its range.
We consider a mobile impurity immersed in a Bose gas at finite temperature. Using perturbation theory valid for weak coupling between the impurity and the bosons, we derive analytical results for the energy and damping of the impurity for low and high temperatures, as well as for temperatures close to the critical temperature Tc{T}_{c}Tc​ for Bose-Einstein condensation. These results show that the properties of the impurity vary strongly with temperature. In particular, the energy exhibits a nonmonotonic behavior close to Tc{T}_{c}Tc​, and the damping rises sharply close to Tc{T}_{c}Tc​. We argue that this behavior is generic for impurities immersed in an environment undergoing a phase transition that breaks a continuous symmetry. Finally, we discuss how these effects can be detected experimentally.
Abstract The properties of a Bose polaron immersed in a dilute two-dimensional medium at finite temperatures are discussed. Assuming that the impurity is weakly coupled to bath particles, we have perturbatively calculated the polaron energy, effective mass, quasiparticle residue and damping rate. The parameters of the impurity spectrum are found to be well-defined in the whole temperature region whereas the pole structure of the impurity Green’s function is visible only at absolute zero. At any finite temperatures the quasiparticle residue is logarithmically-divergent signalling of the branch-cut behavior of the polaron propagator.
We investigate the properties of an impurity 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 aaa, 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 bbb can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where nnn is the density of the bath and mmm is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.
Abstract The properties of an impurity immersed in a dilute D -dimensional Bose gas at temperatures close to its second-order phase transition point are considered. Particularly by means of the 1/ N -expansion, we calculate the leading-order polaron energy and the damping rate in the limit of vanishing boson–boson interaction. It is shown that the perturbative effective mass and the quasiparticle residue diverge logarithmically in the long-length limit, signalling the non-analytic behavior of the impurity spectrum and pole-free structure of the polaron Green’s function in the infrared region, respectively.
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.