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arXiv:2201.04295 · Physical Review A

Strongly interacting impurities in a dilute Bose condensate

Nikolay Yegovtsev, Pietro Massignan, Victor Gurarie

Published Sep 7, 2022• 13 citations
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Abstract

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.

DOI
10.1103/physreva.106.033305

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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.
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 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.
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.
When an impurity is immersed in a Bose-Einstein condensate, impurity-boson interactions are expected to dress the impurity into a quasiparticle, the Bose polaron. We superimpose an ultracold atomic gas of ^{87}Rb with a much lower density gas of fermionic ^{40}K impurities. Through the use of a Feshbach resonance and radio-frequency spectroscopy, we characterize the energy, spectral width, and lifetime of the resultant polaron on both the attractive and the repulsive branches in the strongly interacting regime. The width of the polaron in the attractive branch is narrow compared to its binding energy, even as the two-body scattering length diverges.
An impurity immersed in a Bose condensate can form a quasiparticle known as a Bose polaron. When the impurity-boson interaction is short ranged and three-body Efimov correlations are neglected, the quasiparticle properties can be characterized in terms of the impurity-boson scattering length a IB and the condensate coherence length ξ . This description remains valid irrespective of the bath density n 0 . Long-ranged interactions—such as provided by Rydberg or ionic impurities—introduce an effective interaction range r eff as the third length scale. The interplay among these competing length scales raises the question of whether a robust description across different bath densities can still be maintained. In this study, we discuss the quasiparticle nature of long-range impurities and its dependence on the length scales n 0 − 1 / 3 , r eff , and ξ . We employ two complementary theories—the coherent-state ansatz and the perturbative Gross-Pitaevskii theory—which incorporate beyond-Fröhlich interactions. We derive an analytical expression for the beyond-Fröhlich effective mass for a contact interaction and numerically compute the effective mass for long-range impurities. We argue that the coupling parameter | a IB | n 0 1 / 3 remains the principal parameter governing the properties of the polaron. For weak ( | a IB | n 0 1 / 3 ≪ 1 ) and intermediate ( | a IB | n 0 1 / 3 ≃ 1 ) values of the coupling parameter, long-range impurities in a Bose condensate are well described as quasiparticles with a finite quasiparticle weight and a well-defined effective mass. However, the quasiparticle weight becomes significantly suppressed as the effective impurity volume is occupied by an increasing number of bath particles ( r eff n 0 1 / 3 ≫ 1 ).
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.