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arXiv:1109.1122 · Physical Review A

Many-polaron description of impurities in a Bose-Einstein condensate in the weak-coupling regime

Wim Casteels, Jacques Tempere, J. T. Devreese

Published Dec 9, 2011• 36 citations
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Abstract

The weak-coupling many-polaron formalism is applied to the case of the polaronic system consisting of impurities in a Bose-Einstein condensate. This allows investigating the ground-state properties and the response of the system to Bragg spectroscopy. Then, this theory is applied to the system of spin-polarized fermionic lithium-6 impurities in a sodium condensate. The Bragg spectrum reveals a peak that corresponds to the emission of Bogoliubov excitations. Both the ground-state properties and the response spectrum show that the polaronic effect vanishes at high densities. We also look at two possibilities to define the polaronic effective mass and observe that this results in a different quantitative behavior if multiple impurities are involved.

DOI
10.1103/physreva.84.063612

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The weak-coupling many-polaron formalism is applied to the case of the polaronic system consisting of impurities in a Bose-Einstein condensate. This allows investigating the ground-state properties and the response of the system to Bragg spectroscopy. Then, this theory is applied to the system of spin-polarized fermionic lithium-6 impurities in a sodium condensate. The Bragg spectrum reveals a peak that corresponds to the emission of Bogoliubov excitations. Both the ground-state properties and the response spectrum show that the polaronic effect vanishes at high densities. We also look at two possibilities to define the polaronic effective mass and observe that this results in a different quantitative behavior if multiple impurities are involved.
We expand the existing polaron response theory, expressed within the Mori-Zwanzig projection operator formalism applicable for the transfer of arbitrary energy and zero momentum, for the case of finite momentum exchange. A general formula is then derived that can be used to calculate the response of a system to a probe that transfers both momentum and energy to the system. The main extension of the existing polaron response theory is the finite momentum exchange, which was not needed until now, since it is negligible for optical absorption. However, this formalism is needed to calculate the response of the polaronic system consisting of an impurity in a Bose-Einstein condensate (BEC) to Bragg spectroscopy. We show that the well-known features that appear in the optical absorption of the solid-state Fr\"ohlich polaron are also present in the Bragg response of the BEC-impurity polaron. The f-sum rule is written in a form suitable to provide an independent consistency test for our results. The effect of lifetime broadening on the BEC-impurity spectrum is examined. The results derived here are discussed in the framework of an experimental realization consisting of a lithium impurity in a sodium condensate.
We theoretically investigate the role of multiple impurity atoms on the ground-state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fr\"ohlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fr\"ohlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and the effective mass. These results are examined for system parameters corresponding to two recent experimental realizations of the Bose polaron, one with fermionic impurities and one with bosonic impurities.
The variational Feynman formalism for the polaron, extended to an all-coupling treatment of bipolarons, is applied for two impurity atoms in a Bose-Einstein condensate. This shows that if the polaronic coupling strength is large enough, the impurities will form a bound state (the bipolaron). As a function of the mutual repulsion between the impurities, two types of bipolaron are distinguished: a tightly bound bipolaron at weak repulsion and a dumbbell bipolaron at strong repulsion. Apart from the binding energy, the evolution of the bipolaron radius and its effective mass are also examined as a function of the strength of the repulsive interaction between the impurities and of the polaronic coupling strength. We then apply the strong-coupling formalism to multiple-impurity atoms in a condensate, which leads to the prediction of multipolaron formation in the strong-coupling regime. The results of the two formalisms are compared for two impurities in a condensate, which results in a general qualitative agreement and a quantitative agreement at strong coupling. Typically, the system of impurity atoms in a Bose-Einstein condensate is expected to exhibit the polaronic weak-coupling regime. However, the polaronic coupling strength is, in principle, tunable with a Feshbach resonance.
The application of optical lattices allows a tuning of the geometry of Bose-Einstein condensates to effectively reduced dimensions. In the context of solid-state physics the consideration of the low-dimensional Fr\"ohlich polaron results in an extension of the polaronic strong coupling regime. With this motivation we apply the Jensen-Feynman variational principle to calculate the ground-state properties of the polaron consisting of an impurity in a Bose-Einstein condensate in reduced dimensions. Also the response of this system to Bragg scattering is calculated. We show that reducing the dimension leads to a larger amplitude of the polaronic features and is expected to facilitate the experimental observation of polaronic properties. In optical lattices not only Feshbach resonances but also confinement-induced resonances can be used to tune the polaronic coupling strength. This opens up the possibility to experimentally reveal the intermediate and strong polaronic coupling regimes and resolve outstanding theoretical questions regarding polaron theory.
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.
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.