Ultracold hybrid ion-atom gases represent an exciting frontier for quantum simulation offering a new set of functionalities and control. Here, we study a mobile ion immersed in a Bose-Einstein condensate and show that the long-range nature of the ion-atom interaction gives rise to an intricate interplay between few- and many-body physics. This leads to the existence of several polaronic and molecular states due to the binding of an increasing number of bosons to the ion, which is well beyond what can be described by a short-range pseudopotential. We use a complementary set of techniques including a variational ansatz and field theory to describe this rich physics and calculate the full spectral response of the ion. It follows from thermodynamic arguments that the ion-atom interaction leads to a mesoscopic dressing cloud of the polarons, and a simplified model demonstrates that the spectral weight of the molecules scale with increasing powers of the density. We finally calculate the quantum dynamics of the ion after a quench experiment.
Ultracold hybrid ion-atom gases represent an exciting frontier for quantum simulation offering a new set of functionalities and control. Here, we study a mobile ion immersed in a Bose-Einstein condensate and show that the long-range nature of the ion-atom interaction gives rise to an intricate interplay between few- and many-body physics. This leads to the existence of several polaronic and molecular states due to the binding of an increasing number of bosons to the ion, which is well beyond what can be described by a short-range pseudopotential. We use a complementary set of techniques including a variational ansatz and field theory to describe this rich physics and calculate the full spectral response of the ion. It follows from thermodynamic arguments that the ion-atom interaction leads to a mesoscopic dressing cloud of the polarons, and a simplified model demonstrates that the spectral weight of the molecules scale with increasing powers of the density. We finally calculate the quantum dynamics of the ion after a quench experiment.
The remarkable single-particle control of individual ions combined with the versatility of ultracold atomic gases makes hybrid ion-atom systems an exciting new platform for quantum simulation of few- and many-body quantum physics. Here, we study theoretically the properties of a mobile ion immersed in a quantum degenerate gas of fermionic atoms. Using an effective low-energy atom-ion interaction together with a well-established approach that includes exactly two-body correlations, we calculate the full spectral response of the ion and demonstrate the existence of several quasiparticle branches, which are charged analogs of the Fermi polaron observed in neutral atomic gases. Due to the long-range nature of the atom-ion interaction, these ionic Fermi polarons have several properties distinct from their neutral counterparts such as the simultaneous presence of several stable states and smooth transitions from repulsive to attractive polarons with increasing interaction strength. Surprisingly, the residue of the ionic polaron is shown to increase with the Fermi density for fixed interaction strength, which is in marked contrast with the neutral polaron. The properties of the ionic polaron approach that of the neutral polaron only in the low-density limit where the average interparticle spacing is larger than the characteristic length of the atom-ion interaction. We finally analyze the effects of the Fermi gas on the molecular ions, which are bound atom-dimer states.
We present an in-depth many-body investigation of the so-called mesoscopic molecular ions that can buildup when an ion is immersed into an atomic Bose-Einstein condensate in one dimension. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for mixtures of ultracold bosonic species for solving the underlying many-body Schrödinger equation. This enables us to unravel the actual structure of such massive charged molecules from a microscopic perspective. Laying out their phase diagram with respect to atom number and interatomic interaction strength, we determine the maximal number of atoms bound to the ion and reveal spatial densities and molecular properties. Interestingly, we observe a strong interaction-induced localization, especially for the ion, that we explain by the generation of a large effective mass, similarly to ions in liquid Helium. Finally, we predict the dynamical response of the ion to small perturbations. Our results provide clear evidence for the importance of quantum correlations, as we demonstrate by benchmarking them with wave function ansatz classes employed in the literature.
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.
Abstract The presence of strong interactions in a many-body quantum system can lead to a variety of exotic effects. Here we show that even in a comparatively simple setup consisting of a charged impurity in a weakly interacting bosonic medium the competition of length scales gives rise to a highly correlated mesoscopic state. Using quantum Monte Carlo simulations, we unravel its vastly different polaronic properties compared to neutral quantum impurities. Moreover, we identify a transition between the regime amenable to conventional perturbative treatment in the limit of weak atom-ion interactions and a many-body bound state with vanishing quasi-particle residue composed of hundreds of atoms. In order to analyze the structure of the corresponding states, we examine the atom-ion and atom-atom correlation functions which both show nontrivial properties. Our findings are directly relevant to experiments using hybrid atom-ion setups that have recently attained the ultracold regime.
Bose-Einstein condensation is a macroscopic quantum phenomenon where cooling down a gas of bosonic particles to ultracold temperatures results in the macroscopic occupation of the lowest energy state. This new state of matter has been used as a quantum simulator of many-body phenomena and theories due to its extreme tunability and controllability. An important example of such a many-body system is the polaron which, in its most general form, describes an impurity interacting with a bosonic bath. In the case of ultracold Bose gases, the impurity interacts with and is dressed by the Bogoliubov excitations of the gas. A supersolid is a state of matter that exhibits both superfluidity and crystalline order, which are seemingly irreconcilable properties. It has recently been observed in dipolar ultracold Bose gases, where it arises from the long-range anisotropic dipole-dipole interactions, and also other systems. The breaking of both translational symmetry and gauge symmetry results in multiple excitation modes in the supersolid. In this thesis, the charged Bose polaron and an impurity in a dipolar ultracold Bose gas exhibiting supersolidity (the supersolid Bose polaron) are studied. The ground-state properties of the charged Bose polaron are discussed using a variational path-integral approach. Absorption spectroscopy is proposed as a probe of the charged Bose polaron, and the optical response is studied for weak impurity-boson interactions. Next, the one-dimensional dipolar supersolid Bose polaron is investigated where multiple approaches are used for the derivation of the ground-state properties. The study of the polaron problem with a supersolid background is of particular interest because of the rich excitation spectrum of the supersolid. Interesting phenomena, such as possible localization of the polaron to a single droplet for strong interactions, are observed. The absorption spectrum of a charged impurity in the supersolid is also derived, which, because of the different excitation modes of the supersolid, shows multiple peaks from which information such as the superfluid fraction may be obtained.
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.