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arXiv:2101.08474

Polarons in a ferromagnetic spinor Bose-Einstein condensates

Xiao-Lu Yu, Boyang Liu

Published Jan 21, 2021• 0 citations
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Abstract

We investigate the polarons formed by immersing a spinor impurity in a ferromagnetic state of $F=1$ spinor Bose-Einstein condensate. The ground state energies and effective masses of the polarons are calculated in both weak-coupling regime and strong-coupling regime. In the weakly interacting regime the second order perturbation theory is performed. In the strong coupling regime we use a simple variational treatment. The analytical approximations to the energy and effective mass of the polarons are constructed. Especially, a transition from the mobile state to the self-trapping state of the polaron in the strong coupling regime is discussed. We also estimate the signatures of polaron effects in spinor BEC for the future experiments.

DOI
10.48550/arxiv.2101.08474

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We investigate the polarons formed by immersing a spinor impurity in a ferromagnetic state of F=1F=1F=1 spinor Bose-Einstein condensate. The ground state energies and effective masses of the polarons are calculated in both weak-coupling regime and strong-coupling regime. In the weakly interacting regime the second order perturbation theory is performed. In the strong coupling regime we use a simple variational treatment. The analytical approximations to the energy and effective mass of the polarons are constructed. Especially, a transition from the mobile state to the self-trapping state of the polaron in the strong coupling regime is discussed. We also estimate the signatures of polaron effects in spinor BEC for the future experiments.
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.
We use a nonperturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fr\"ohlich Hamiltonian with renormalized parameters is possible. Its strong-coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud.
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 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.
Bose polarons, quasiparticles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a nonperturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities and in this way minimizes quantum fluctuations. The mean-field equations are solved exactly in the Born-Oppenheimer approximation, leading to an analytic expression for the interaction potential of heavy polarons, which is found to be in excellent agreement with quantum Monte Carlo (QMC) results. In the strong coupling limit, the potential substantially deviates from the exponential form valid for weak coupling and has a linear shape at short distances. Taking into account the leading-order Born-Huang corrections, we calculate bipolaron binding energies for impurity-boson mass ratios as low as 3 and find excellent agreement with QMC results.