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.
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.
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.
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.
When an impurity interacts with a bath of phonons it forms a polaron. For increasing interaction strengths the mass of the polaron increases and it can become self-trapped. For impurity atoms inside an atomic Bose-Einstein condensate (BEC) the nature of this transition is not understood. While Feynman's variational approach to the Fröhlich model predicts a sharp transition for light impurities, renormalization group studies always predict an extended intermediate-coupling region characterized by large phonon correlations. To investigate this intricate regime and to test polaron physics beyond the validity of the Fröhlich model we suggest a versatile experimental setup that allows us to tune both the mass of the impurity and its interactions with the BEC. The impurity is realized as a dark-state polariton (DSP) inside a quasi-two-dimensional BEC. We show that its interactions with the Bogoliubov phonons lead to photonic polarons, described by the Bogoliubov-Fröhlich Hamiltonian, and make theoretical predictions using an extension of a recently introduced renormalization group approach to Fröhlich polarons.
Abstract Lattice polarons, quasiparticles arising from the interaction between an impurity and its surrounding bosonic environment confined to a lattice system, have emerged as a platform for generating complex few-body states, probing many-body phenomena, and addressing long-standing problems in physics. In this study, we employ a variational ansatz to investigate the quasiparticle and spectral properties of an impurity coupled to a condensate gas of hard-core bosons in a two-dimensional optical lattice. Our findings demonstrate that the polaron features can be tuned by adjusting the filling factor of the bath, revealing intriguing polaron characteristics in the strongly interacting regime. These results offer valuable insights for lattice polaron experiments with ultracold gases and can serve as a guide for new experiments in emergent quantum devices, such as moiré materials, where optical excitations can be described in terms of hard-core bosons.
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.
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fröhlich Hamiltonian that applies at weak couplings. Already this highly simplified model allows insights into ultra-violet divergencies, logarithmic and power-law, that need to be properly regularized. To capture the physics near a Feshbach resonance, two-phonon scattering terms on the impurity as well as phonon-phonon interactions need to be included. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems, ranging from Lee-Low-Pines mean-field theory, Chevy-ansatz, Gross-Pitaevskii-equation to diagrammatic Monte Carlo approaches. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional 1D and 2D quantum systems; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.