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arXiv:2410.09413

Impurities and polarons in bosonic quantum gases: a review on recent progress

Fabian Grusdt, Nader Mostaan, Eugene Demler, Luis A. Peña Ardila

Published Oct 12, 2024• 0 citations
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Abstract

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 (BEC) 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. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency (RF) 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; 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.

DOI
10.48550/arxiv.2410.09413

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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 (BEC) 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. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency (RF) 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; 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.
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.
The Fröhlich polaron model describes a ubiquitous class of problems concerned with understanding properties of a single mobile particle interacting with a bosonic reservoir. Originally introduced in the context of electrons interacting with phonons in crystals, this model found applications in such diverse areas as strongly correlated electron systems, quantum information, and high energy physics. In the last few years this model has been applied to describe impurity atoms immersed in Bose-Einstein condensates of ultracold atoms. The tunability of microscopic parameters in ensembles of ultracold atoms and the rich experimental toolbox of atomic physics should allow to test many theoretical predictions and give us new insights into equilibrium and dynamical properties of polarons. In these lecture notes we provide an overview of common theoretical approaches that have been used to study BEC polarons, including Rayleigh-Schrödinger and Green's function perturbation theories, self-consistent Born approximation, mean-field approach, Feynman's variational path integral approach, Monte Carlo simulations, renormalization group calculations, and Gaussian variational ansatz. We focus on the renormalization group approach and provide details of analysis that have not been presented in earlier publications. We show that this method helps to resolve striking discrepancy in polaron energies obtained using mean-field approximation and Monte Carlo simulations. We also discuss applications of this method to the calculation of the effective mass of BEC polarons. As one experimentally relevant example of a non-equililbrium problem we consider Bloch oscillations of Bose polarons and demonstrate that one should find considerable deviations from the commonly accepted phenomenological Esaki-Tsu model. We review which parameter regimes of Bose polarons can be achieved in various atomic mixtures.
Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.
Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.
In this work we provide a comprehensive review of theoretical and experimental studies of the properties of polarons formed by mobile impurities strongly interacting with quantum many-body systems. We present a unified perspective on the universal concepts and theoretical techniques used to characterize polarons in two distinct platforms, ultracold atomic gases and atomically-thin transition metal dichalcogenides, which are linked by many deep parallels. We review polarons in both fermionic and bosonic environments, highlighting their similarities and differences including the intricate interplay between few- and many-body physics. Various kinds of polarons with long-range interactions or in magnetic backgrounds are discussed, and the theoretical and experimental progress towards understanding interactions between polarons is described. We outline how polaron physics, regarded as the low density limit of quantum mixtures, provides fundamental insights regarding the phase diagram of complex condensed matter systems. Furthermore, we describe how polarons may serve as quantum sensors of many-body physics in complex environments. Our work highlights the open problems, identifies new research directions and provides a comprehensive framework for this rapidly evolving research field.
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.