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Chinese Physics Letters

Polaron in Bose–Einstein–Condensation System

Huang Bei-Bing, Shaolong Wan

Published Aug 1, 2009• 28 citations
Publisher

Abstract

We consider the motion of an impurity in a Bose–Einstein condensate system at T = 0 K with the contact interactions for boson-boson and boson-impurity. Under the forward-scattering approximation, we obtain a Fröhlich-like Hamiltonian for this system, which means that a polaron can be formed. The effective mass, the phonon number and the energy to form a polaron are obtained. We also discuss the validity of the forward-scattering approximation for this system.

DOI
10.1088/0256-307x/26/8/080302

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We consider the motion of an impurity in a Bose–Einstein condensate system at T = 0 K with the contact interactions for boson-boson and boson-impurity. Under the forward-scattering approximation, we obtain a Fröhlich-like Hamiltonian for this system, which means that a polaron can be formed. The effective mass, the phonon number and the energy to form a polaron are obtained. We also discuss the validity of the forward-scattering approximation for this system.
In this paper we study an impurity in Bose-Einstein-Condensate system at T=0KT=0KT=0K and suppose the contact forms for boson-boson and boson-impurity interactions. Using Bogoliubov theory and a further approximation corresponding to only think over the forward scattering of impurity by bosons, we derive a reduced Hamiltonian whose form is the same as the Fröhlich Hamiltonian for large polaron. By using Lee-Low-Pines (LLP) theory for large polaron, we obtain the effective mass of impurity, the phonon number carried by impurity and the energy related to the existence of impurity. In addition, we also discuss the valid range for forward-scattering approximation.
Abstract Bose polarons are quasiparticles formed through the interaction between impurities and Bose–Einstein condensates. In this paper, we derive an effective Fröhlich Hamiltonian using the generalized Bogoliubov transformation. The effective Fröhlich Hamiltonian encompasses two types of effective interactions: impurity-density (ID) coupling and impurity-spin (IS) coupling. Furthermore, we employ the Lee–Low–Pines variational approach to investigate the relevant properties of Bose polarons induced by the ID and IS coupling. These properties include the ground state energy, effective mass, and average number of virtual phonons. Our findings reveal that the contribution resulting from IS couplings to the ground energy decreases to zero near the miscible–immiscible boundary. Additionally, the increase of the IS coupling induces a greater number of virtual phonons, impeding the movement of impurities and leading to a significant increase in the effective mass of Bose polarons.
The description of an impurity atom in a Bose-Einstein condensate can be cast in the form of Fr\"ohlich's polaron Hamiltonian, where the Bogoliubov excitations play the role of the phonons. An expression for the corresponding polaronic coupling strength is derived, relating the coupling strength to the scattering lengths, the trap size and the number of Bose condensed atoms. This allows to identify several approaches to reach the strong-coupling limit for the quantum gas polarons, whereas this limit was hitherto experimentally inaccessible in solids. We apply Feynman's path-integral method to calculate for all coupling strengths the polaronic shift in the free energy and the increase in the effective mass. The effect of temperature on these quantities is included in the description. We find similarities to the acoustic polaron results and indications of a transition between free polarons and self-trapped polarons. The prospects, based on the current theory, of investigating the polaron physics with ultracold gases are discussed for lithium atoms in a sodium condensate.
This study investigates the polaron states formed by an impurity immersed in a spin-1 spinor Bose-Einstein condensate. Employing the Fröhlich Hamiltonian framework, we systematically calculated the ground-state energy and effective mass of polarons in both weak-coupling and strong-coupling regimes. For the weakly interacting regime, the analysis was conducted using second-order perturbation theory. In the strong-coupling regime, we constructed an analytical approximation for the polaron states and performed variational calculations to determine their energy and effective mass. Furthermore, we discussed the transition from the mobile state to the self-trapped state of the polaron in the strong-coupling region. We also estimate the signatures of polaron effects in spinor BEC for the future experiments.
When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.
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.